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The equation for all values of x by completing the square, x²-15=-4x

User Labyrinth
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1 Answer

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Solve for x over the real numbers:

x^2 - 15 = -4 x

Add 4 x to both sides:

x^2 + 4 x - 15 = 0

Add 15 to both sides:

x^2 + 4 x = 15

Add 4 to both sides:

x^2 + 4 x + 4 = 19

Write the left hand side as a square:

(x + 2)^2 = 19

Take the square root of both sides:

x + 2 = sqrt(19) or x + 2 = -sqrt(19)

Subtract 2 from both sides:

x = sqrt(19) - 2 or x + 2 = -sqrt(19)

Subtract 2 from both sides:

Answer: x = sqrt(19) - 2 or x = -2 - sqrt(19)

User Johannes Metzner
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