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Solve x^2 + 4x = 1 for x by completing the square.

x = −3
x = −1
x equals plus or minus square root of 5 minus 2
x equals plus or minus square root of 5 plus 2

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2 votes

Answer:

x equals plus or minus square root of 5 minus 2

Explanation:

Let's solve your equation step-by-step.

x²+4x=1

Step 1: Subtract 1 from both sides.

x²+4x−1=1−1

x²+4x−1=0

For this equation: a=1, b=4, c=-1

1x²+4x+−1=0

Step 2: Use quadratic formula with a=1, b=4, c=-1.


\sf \: x = \frac{−b± \sqrt{ b {}^(2) −4ac}}{2a}


\sf \: x = \frac{−(4)± \sqrt{4 {}^(2) −4(1)( - 1)}}{2(1)}


\sf \: x = (−4±√20)/(2)

x=−2+√5 or x=−2−√5

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