If using the method of completing the square to solve the quadratic equation
x2 + 13x -3 = 0, which number would have to be added to "complete the
square"?

Answer:

Step-by-step explanation:

The term added which completes the square is half of the linear coefficient squared. In a quadratic ax^2+bx+c, b is the linear coefficient, so in this case the added term would be

(13/2)^2=169/4=42.25

The term 13/2 is added to complete the square.

A quadratic equation is a polynomial which has the highest degree equal to two. It is a second-degree equation of the form ax² + bx + c = 0, where a, b, are the coefficients, c is the constant term, and x is the variable.

For the given situation,

The quadratic equation is x^2 + 13x -3 = 0.

This is not the perfect square term. So we can solve this by using the completing the square method.

⇒ [tex]x^{2} +13x-3=0[/tex]

⇒ [tex]x^{2} +13x=3[/tex]

⇒ [tex]x^{2} +13x + (\frac{13}{2})^{2} =3+(\frac{13}{2})^{2}[/tex]

⇒ [tex](x+\frac{13}{2} )^{2} =3+\frac{169}{4}[/tex]

⇒ [tex](x+\frac{13}{2} )^{2} =\frac{181}{4}[/tex]

⇒ [tex]\sqrt{ (x+\frac{13}{2} )}^{2} =\sqrt{\frac{181}{4}}[/tex]

⇒ [tex](x+\frac{13}{2})[/tex] = ± [tex]\frac{\sqrt{181} }{2}[/tex]

Hence  we can conclude that the term 13/2 is added to complete the square.

Learn more about quadratic equations here

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