Question

question
solve the equation for all values of x by completing the square.
$2x^2 + 40x = -174$
answer attempt 1 out of 2
+ additional solution - no solution

Explanation:

Step1: Divide by coefficient of \(x^2\)

Divide the entire equation \(2x^2 + 40x = -174\) by 2 to make the coefficient of \(x^2\) equal to 1.
\(\frac{2x^2}{2}+\frac{40x}{2}=\frac{-174}{2}\)
\(x^2 + 20x = -87\)

Step2: Complete the square

Take half of the coefficient of \(x\) (which is 20), square it, and add it to both sides. Half of 20 is 10, and \(10^2 = 100\).
\(x^2 + 20x + 100 = -87 + 100\)
\((x + 10)^2 = 13\)

Step3: Solve for \(x\)

Take the square root of both sides. Remember to consider both the positive and negative square roots.
\(x + 10 = \pm\sqrt{13}\)
Subtract 10 from both sides to solve for \(x\).
\(x = -10 \pm\sqrt{13}\)

Answer:

\(x = -10 + \sqrt{13}\) or \(x = -10 - \sqrt{13}\)