Question

What is the only solution of 2x2 + 8x = x2 – 16?

Answer 1

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Equation Given
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$2x^2 + 8x = x^2 -16$

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Subtract x² + 16 from both sides
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$2x^2 -x^2 + 8x + 16 = 0$

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Combine like terms
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$x^2 + 8x + 16 = 0$

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Factorize
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$(x + 4)^2 = 0$

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Square root both sides
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$x + 4 = 0$

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Take away 4 from both sides
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$x = - 4$

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Answer: x =  - 4
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Answer 2

Hello there!

2x² + 8x = x² - 16

Let start by subtracting x² - 16 on both sides

2x² + 8x - x² - 16 = x² - 16 - x² - 16

x² + 8x - 16 = 0

Now we can factorize the left side

(x + 4)(x + 4) = 0

Set factors equal to 0

x + 4 = 0 or x + 4 = 0

x = 0 - 4 or x = 0 - 4

x = -4

Thus,

The only solution is -4

As always, it is my pleasure to help students like you!