Question

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

Answer 1

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