Question

If using the method of completing the square to solve the quadratic equation x^2+9x+35=0 which number would have to be added to "complete the square"?

Answer 1

Answer:

$x = -4.5 \pm \sqrt{-14.75}$

Step-by-step explanation:

A quadratic equation is given to us and we need to solve the equation by completing the square. The given equation is ,

$\sf\implies x^2+9x+35=0$

Here the coefficient of x is already 1. And the coefficient of x is 9 . Hence on dividing and multiplying by 2 ,we have ;

$\sf\implies x^2+\bigg(\dfrac{9}{2}\bigg) (2)(x) + 35 = 0$

Now adding and subtracting (9/2)² , we have ;

$\sf\implies \bigg[ x^2+\bigg(\dfrac{9}{2}\bigg)^2+2(x)\bigg(\dfrac{9}{2}\bigg) \bigg] -\bigg(\dfrac{9}{2}\bigg)^2+ 35 = 0$

Now the terms inside the big brackets are in the form of ( a + b)² = a² + b² + 2ab , so that ;

$\sf\implies \bigg( x +\dfrac{9}{2}\bigg)^2 = \dfrac{81}{4}-35$

Simplify the LHS ,

$\sf\implies \bigg( x +\dfrac{9}{2}\bigg)^2 = \dfrac{81-140}{4}\\\\\sf\implies\bigg( x +\dfrac{9}{2}\bigg)^2 = \dfrac{-59}{4}$

Square rooting both sides ,

$\sf\implies x + 4.5 = \pm \sqrt{-14.75}$

Subtracting 4.5 to both sides ,

$\implies\boxed{\pink{\frak{ x = -4.5 \pm \sqrt{-14.75}}}}$