Question

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solve the equation for all values of x by completing the square. express your answer in simplest form.
$x^2 + 2x = 14$
answer
attempt 1 out of 3
+ additional solution - no solution
$x = $
submit answer

Explanation:

Step1: Complete the square

Take half of the coefficient of $x$, square it, and add to both sides. The coefficient of $x$ is 2, half is 1, square is 1.
$x^2 + 2x + 1 = 14 + 1$

Step2: Rewrite as perfect square

Left side is a perfect square trinomial, right side simplifies.
$(x + 1)^2 = 15$

Step3: Take square roots

Take square root of both sides, include $\pm$ for both roots.
$x + 1 = \pm\sqrt{15}$

Step4: Isolate x

Subtract 1 from both sides to solve for x.
$x = -1 \pm\sqrt{15}$

Answer:

$x = -1 + \sqrt{15}$ and $x = -1 - \sqrt{15}$