The square of an integer is 5 more than 4 times the integer. Find the integer.

Answer:

The integer can be -1 or 5.

Step-by-step explanation:

Let an integer is x.

ATQ,

The square of an integer is 5 more than 4 times the integer.

[tex]x^2=5+4x[/tex]

or

[tex]x^2-5-4x=0\\\\x^2-4x-5=0[/tex]

It is a quadratic equation. Using middle term splitting,

[tex]x^2-5x+x-5=0\\\\x(x-5)+1(x-5)=0\\\\(x+1)(x-5)=0\\\\x=-1,5[/tex]

So, the integer can be -1 or 5.

If the square of an integer is 5 more than 4 times the integer, the integers are -1 and 5

Let the unkown integer be "x"

The square of an integer is expressed as x^2

5 more than 4 times the integer is expressed as [tex]4x +5[/tex]

Equate both expressions to have:

[tex]x^2 = 4x + 5\\[/tex]

Equate to zero and factorize:

x^2 - 4x - 5  = 0

x^2 - 5x + x - 5 = 0

x(x - 5) + 1(x - 5) = 0

(x + 1)(x - 5) = 0

x = -1 and 5

Hence the integers are -1 and 5

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