Question

Use the quadratic formula to solve 9x2 + 6x – 17 = 0

Answer 1

The standard form of a quadratic equation is :

ax² + bx + c = 0

And the quadratic formula is:

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$.

So, first step is to compare the given equation with the above equation to get the value of a, b and c.

So, a = 9, b = 6 and c = - 17.

Next step is to plug in these values in the above formula. Therefore,

$x=\frac{-6\pm\sqrt{6^2-4*(9)*(-17)}}{2*9}$

$=\frac{-6\pm\sqrt{36+612}}{18}$

$=\frac{-6\pm\sqrt{648}}{18}$

$=\frac{-6\pm\sqrt{324*2}}{18}$

$=\frac{-6\pm\sqrt{324}*\sqrt{2}}{18}$

$=\frac{-6\pm18*\sqrt{2}}{18}$

$=-\frac{6}{18} \pm\frac{18\sqrt{2}}{18}$

$=-\frac{1}{3} \pm\sqrt{2}$.

So, x = $-\frac{1}{3} \pm\sqrt{2}$