Answer
$x\approx 1.92$ and $x\approx -9.92$.
Work Step by Step
The given equation is
$\Rightarrow -3x^2-24x+17=-40$
Subtract $17$ from each side.
$\Rightarrow -3x^2-24x+17-17=-40-17$
Simplify.
$\Rightarrow -3x^2-24x=-57$
Divide each side by $-3$.
$\Rightarrow x^2+8x=19$
Find the value of $(\frac{b}{2})^2$.
Substitute $8$ for $b$.
$=(\frac{8}{2})^2$
Simplify.
$=(4)^2$
$=16$
Add $16$ to each side of the equation.
$\Rightarrow x^2+8x+16=19+16$
Simplify.
$\Rightarrow x^2+8x+16=35$
Write the left side as the square of a binomial.
$\Rightarrow (x+4)^2=35$
Take the square root of each side.
$\Rightarrow x+4=\pm \sqrt{35}$
Subtract $4$ from each side.
$\Rightarrow x+4-4=\pm\sqrt{35}-4$
Simplify.
$\Rightarrow x=\pm\sqrt{35}-4$
The solutions are $x=\sqrt{35}-4\approx 1.92$ and $x=-\sqrt{35}-4\approx -9.92$.
