Question

Some of the steps for completing the square to solve x2 + 5x = 2 are shown. x2 + 5x = 2 x2 + 5x + = 2 + Which are solutions of x2 + 5x = 2? Check all that apply.

Answer 1

The solutions would be +0.37 and -0.37.

When completing the square, we take 1/2 of the value of b (in this case 5).  5/2=2.5.  We then square this number:  2.5²=6.25.  We add this value to both sides of the equation:

x²+5x+6.25 = 2+6.25
(x+2.5)² = 8.25

Take the square root of both sides:
√(x+2.5)² = √8.25
x + 2.5 = 2.87

Subtract 2.5 from both sides:"
x+2.5-2.5 = 2.87-2.5
x = 0.37

We have to take the positive and negative values for solutions, however, since a square root has both positive and negative answers.

Answer 2

Answer:

The solutions would be +0.37 and -0.37.

When completing the square, we take 1/2 of the value of b (in this case 5).  5/2=2.5.  We then square this number:  2.5²=6.25.  We add this value to both sides of the equation:

x²+5x+6.25 = 2+6.25

(x+2.5)² = 8.25

Take the square root of both sides:

√(x+2.5)² = √8.25

x + 2.5 = 2.87

Subtract 2.5 from both sides:"

x+2.5-2.5 = 2.87-2.5

x = 0.37

We have to take the positive and negative values for solutions, however, since a square root has both positive and negative answers.

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Step-by-step explanation: