Please help me to solve this!​

Answer:

For quadratic equations that cannot be solved by factorising, we use a method which can solve ALL quadratic equations called completing the square. We use this later when studying circles in plane analytic geometry.

Completing the square comes from considering the special formulas that we met in Square of a sum and square of a difference earlier:

(x + y)2 = x2 + 2xy + y2 (Square of a sum)

(x − y)2 = x2 − 2xy + y2 (Square of a difference)

To find the roots of a quadratic equation in the form:

\displaystyle{a}{x}^{2}+{b}{x}+{c}={0}ax

2

+bx+c=0,

follow these steps:

(i) If a does not equal \displaystyle{1}1, divide each side by a (so that the coefficient of the x2 is \displaystyle{1}1).

(ii) Rewrite the equation with the constant term on the right side.

(iii) Complete the square by adding the square of one-half of the coefficient of x to both sides.

(iv) Write the left side as a square and simplify the right side.

(v) Equate and solve.

Example 1

Find the roots of x2 + 10x − 4 = 0 using completing the square method.

Answer

Example 2

Solve 4x2 + x = 3 by completing the square.

Answer

Exercises

Solve the following quadratic equations by completing the square

Q1. \displaystyle{2}{s}^{2}+{5}{s}={3}2s

2

+5s=3Answer

Q2. \displaystyle{3}{x}^{2}={3}-{4}{x}3x

2

=3−4xAnswer

Q3. \displaystyle{9}{v}^{2}-{6}{v}-{2}={0}9v

2

−6v−2=0Answer

Q4. \displaystyle{a}{x}^{2}+{b}{x}+{c}={0}ax

2

+bx+c=0Answer

1. Solving Quadratic Equations by Factoring

3. The Quadratic Formula

Step-by-step explanation:

step 1. f(x) = 5x^2 + 20x + 20

step 2. f(x) = 5(x^2 + 4x + 4)

step 3. f(x) = 5(x + 2)^2

step 4. 0 = 5(x + 2)^2

step 5. zeros: -2

Answer: r≈ 9.99ft

Using the formula

C=2 π r

Solving for r

r= C/2π = 62.8/2·π ≈9.99493ft

Answer:

Are you guys classmates?

Answer:

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form

y*x=k or y= k/x

in this problem we have that

the value of the constant K is equal to 8

so

pv=8

Solve for V

v=8/p

Find the value of V for p=4

substitute the value of P in the formula

v=8/4=2

therefore

the answer is

the value of V is equal to 2

Answer:

-4.24264069; -4.2 (nearest tenth); -4.24 (nearet hundreths)

Step-by-step explanation:

square root of 72 = 8.48528137 or 8.5 (rounding to tenths)

square root of 2 = 1.41421356 or 1.4

square root of 128 = 11.3137085 or 11.3

Answer:

60 miles per hour

Step-by-step explanation:

360 miles / 6 hours = 60 miles per hour

Answer:

60, I hope this helped and please mark brainliest!

Step-by-step explanation:

This would be 60 miles per hour since you divide 360 by 6. So the rate is 60.

Answer:

The answer are 1_ ASA

2_ SSS

3_ SAS

Answer:

-1

Step-by-step explanation:

-12 + 2t = -14

12 + -12 + 2t = -14 + 12

2t = -2

2t/2 = -2/2

t = -1

OOPS my submitted answer was wrong.

Submitting this is so you can give other person points! :]

Answer:

Step-by-step explanation:

(27 - 23)/(8 - 4)= 4/4= 1

y - 23 = x - 4

y = x + 19

Answer:

2x-y=0

Step-by-step explanation:

Answer:

A) Triangle PQR

Step-by-step explanation:

This is the correct triangle because it has the exact same measurements as Triangle ABC. Angles A and P are the same angle on the triangles and they have the same measure (70). Angles C and R are the same angle on the triangles and they have the same measure (75). To solve for Angle C in Triangle ABC though, add angles 70 + 35 together to get 105. A triangle has a total measure of 180, so subtract 180 - 105 to get 75.

Hope it helps!

Answer: Linear functions have a constant slope, while exponential functions start flat and get steeper

Step-by-step explanation: I just took the quiz so I know it’s right. I hope this helps :)

Answer:

Answer: Linear functions have a constant slope, while exponential functions start flat and get steeper

Step-by-step explanation:

I took the test

Answer:

The cost of 1 scarf is $12.25 each.

Step-by-step explanation:

Answer:

akismsksksialoalqoq kskw! sola skkss

Step-by-step explanation:

smksmskkwow!skkw

Answer: 16

Step-by-step explanation: 16 is how much the breaking pad is produced per hour because if you divide all of them you get 16 for each of them on the table

Answer:

12w=12 divided by 2

12w=6

=2

Step-by-step explanation:

Answer:

y

Step-by-step explanation:

2y-y=y

Answer: 2y-y can be written as y because 2y means you have 2 y’s and 2y’s minus 1 y is just 1 y

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

It's the third option.

Step-by-step explanation:

Because if [tex]\frac{7}{10}[/tex] was converted into a decimal it would be 0.7 plus 666, it would be 666.7

Answer:

it's the 3rd one

Answer:

3.0258

Step-by-step explanation:

50.43*6%=3.0258

Step-by-step explanation:

X=49-18/13

X=31/13

X=2.38

so nearest 100 th would be 2.4

Answer: THE ANSWER WOULD BE A. (-5, -18)

Notice how y=4x%2B2 is in slope-intercept form y=mx%2Bb where m is the slope and b is the y-intercept.

So this shows us that the slope is m=4 and the y-intercept is b=2 which is the point (0,2)

You can always plot an equation like this to find intercepts

and slope. Each point requires an x and a y. My

way is to make x+=+0 and find y,

then I make y+=+0 and find x

y+=+4x+%2B+2

y+=+4%2A0+%2B+2 solve for y

y+=+2

the point is (0,2)

then,

0+=+4x+%2B+2 solve for x

subtract 2 from both sides

4x+=+-2

x+=+-%281%2F2%29

the point is (-%281%2F2%29,0)  

Once you have any two points, you can draw the line by connecting them

When the equation is in the form

y+=+mx+%2B+b

m = slope

b = y-intercept

So, your equation y+=+4x+%2B+2

m+=+4 (slope)

b+=+2 (y-intercept)

Step-by-step explanation:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Point Form:  (

−

5

,

−

18

)

Equation Form:  x

=

−

5

,

y

=

−

18

Answer:30 percent something like that

Step-by-step explanation:

Answer:

3x² + 10x - 48

Step-by-step explanation:

Given

(x + 6)(3x - 8)

Each term in the second factor is multiplied by each term in the first factor, that is

x(3x - 8) + 6(3x - 8) ← distribute both parenthesis

= 3x² - 8x + 18x - 48 ← collect like terms

= 3x² + 10x - 48

Answer:

-3

Step-by-step explanation:

To find slope use the equation [tex]y2 - y1 / x2 - x1[/tex]

1. Pick any two coordinate pairs to use in the equation. I'll choose (-2, 7) and (-1, 4).

2. Plug these coordinates into the formula. 4 - 7 / -1 - - 2

3.  Solve! -3/ 1 =  -3

4. The slope of this line is -3