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Solve the equations for all values of x by completing the square x^2+62=-16x

User Jaybit
by
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1 Answer

4 votes

Answer:


x = √(2) - 8\\x = -√(2) - 8

Explanation:

To complete the square, we first have to get our equation into
ax^2 + bx = c form.

First we add 16x to both sides:


x^2 + 16x + 62 = 0

And now we subtract 62 from both sides.


x^2 + 16x = -62

We now have to add
((b)/(2))^2 to both sides of the equation. b is 16, so this value becomes
(16/2)^2 = 8^2 = 64.


x^2 + 16x + 64 = -62+64

We can now write the left side of the equation as a perfect square. We know that x+8 will be the solution because
8\cdot8=64 and
8+8=16.


(x+8)^2 = -62 + 64

We can now take the square root of both sides.


x+8 = √(-62+64)\\\\ x+8 = \pm √(2)

We can now isolate x on one side by subtracting 8 from both sides.


x = \pm√(2) - 8

So our solutions are


x = √(2) - 8\\x = -√(2) - 8

Hope this helped!

User Abhijith Konnayil
by
7.6k points

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