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* 9}}{2} \\`

Square 11.

`\sf \: x=(-11±√(121-4* 9))/(2) \\`

Multiply -4 times 9.

`\sf \: x=(-11±√(121-36))/(2) \\`

Add 121 to -36.

`\sf \: x=(-11±√(85))/(2) \\`

Now solve the equation
`\sf\:x=(-11±√(85))/(2)` when ± is plus. Add -11 to √85.

`\boxed{ \boxed{\bf \: x=(√(85)-11)/(2) }}`

Now solve the equation
`\sf\:x=(-11±√(85))/(2)` when ± is minus. Subtract √85 from -11.

`\boxed{ \boxed{\bf \: x=(-√(85)-11)/(2)} } \\`

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

`\bf \: x=(√(85)-11)/(2) \\ \\ \sf \: and \\ \\ \bf \: x=(-√(85)-11)/(2)`