Question

Solve the equation using the quadratic formula. x^2+ 11x + 9 = 0 The solution set is

Answer 1

$\huge \boxed{\mathfrak{Question} \downarrow}$

Solve the equation using the quadratic formula ⇨ x² + 11x + 9 = 0

$\large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}$

$\sf \: x ^ { 2 } + 11 x + 9 = 0$

All equations of the form $\sf\:ax^{2}+bx+c=0$ can be solved using the quadratic formula: $\sf\frac{-b±\sqrt{b^{2}-4ac}}{2a}$. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$\sf \: x^{2}+11x+9=0$

This equation is in standard form: ax² + bx + c = 0. Substitute 1 for a, 11 for b and 9 for c in the quadratic formula $\sf\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$\sf \: x=\frac{-11±\sqrt{11^{2}-4\times 9}}{2}$

Square 11.

$\sf \: x=\frac{-11±\sqrt{121-4\times 9}}{2}$

Multiply -4 times 9.

$\sf \: x=\frac{-11±\sqrt{121-36}}{2}$

Add 121 to -36.

$\sf \: x=\frac{-11±\sqrt{85}}{2}$

Now solve the equation $\sf\:x=\frac{-11±\sqrt{85}}{2}$ when ± is plus. Add -11 to √85.

$\boxed{ \boxed{\bf \: x=\frac{\sqrt{85}-11}{2} }}$

Now solve the equation $\sf\:x=\frac{-11±\sqrt{85}}{2}$ when ± is minus. Subtract √85 from -11.

$\boxed{ \boxed{\bf \: x=\frac{-\sqrt{85}-11}{2}} }$

The equation is now solved. The solution set is :-

$\bf \: x=\frac{\sqrt{85}-11}{2} \\ \\ \sf \: and \\ \\ \bf \: x=\frac{-\sqrt{85}-11}{2}$