Solve for x . x^2+6x+6=0

Question

asked Apr 24, 2021 39.2k views

1 Answer

Paul Hannon · Answer 1 · 2021-04-29T07:25:53+0000

Answer:

$\boxed {x = √(3) - 3}$

$\boxed {x = -√(3) - 3}$

Explanation:

Solve for the value of
:

x^2 + 6x + 6 = 0

-When you use the quadratic formula (
$\frac{-b\pm \sqrt{b^(2) - 4ac}}{2a}$ ), it would give you two solutions. So, use the quadratic formula:

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

-Simplify
by the exponent
:

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

$x = (-6\pm √(36 - 4 * 6))/(2)$

-Multiply both
and
:

$x = (-6\pm √(36 - 4 * 6))/(2)$

$x = (-6\pm √(36 - 24))/(2)$

-Add
and
:

$x = (-6\pm √(36 - 24))/(2)$

$x = (-6\pm √(12))/(2)$

-Take the square root of
:

$x = (-6\pm √(12))/(2)$

$x = (-6\pm 2√(3))/(2)$

-Now solve the equation when
$\pm$ is plus, So, add
to
2√(3) :

$x = (-6\pm 2√(3))/(2)$

x = (2√(3) - 6)/(2)

-Divide
-6 + 2√(3) both sides by
:

x = (2√(3) - 6)/(2)

$\boxed {x = √(3) - 3}$ (Answer 1)

-Now solve the equation when
$\pm$ is minus. So, Subtract
2√(3) from
:

x = (-2√(3) - 6)/(2)

-Divide
-2√(3) - 6 by
:

x = (-2√(3) - 6)/(2)

$\boxed {x = -√(3) - 3}$ (Answer 2)