Question

solve for u by completing the square.
-2u² - 28u - 14 = 0
show your work here
hint: to add the square root symbol (√□), type
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Explanation:

Step1: Divide by -2

Divide each term by -2:
$\frac{-2u^2}{-2} + \frac{-28u}{-2} + \frac{-14}{-2} = \frac{0}{-2}$
Simplify: $u^2 + 14u + 7 = 0$

Step2: Isolate $u^2$ and $u$ terms

Subtract 7: $u^2 + 14u = -7$

Step3: Complete the square

Take half of 14 (which is 7), square it (49), add to both sides:
$u^2 + 14u + 49 = -7 + 49$
Left side is $(u + 7)^2$, right side is 42:
$(u + 7)^2 = 42$

Step4: Take square roots

Take square root of both sides:
$u + 7 = \pm \sqrt{42}$

Step5: Solve for u

Subtract 7: $u = -7 \pm \sqrt{42}$

Answer:

$u = -7 + \sqrt{42}$ or $u = -7 - \sqrt{42}$