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Solve the following equation by completing the square:

1/4x^2 +x + 1/4


A.

x = -2 + square root of 3 or x = 2 - square root of 3

B.

x = 2 + square root of 3 or x = 2 - square root of 3

C.

x = -2 + square root of 3 or x = -2 - square root of 3

D.

x= 1 or x = -5

Respuesta :

joseaaronlara

Answer:

The answer to your question is letter C.

Step-by-step explanation:

Equation

                          [tex]\frac{1}{4}x^{2} + x + \frac{1}{4}[/tex]

Process

1.- Multiply the equation by 4

                         [tex]4[\frac{1}{4} x^{2} + x + \frac{1}{4}][/tex]

Simplify

                            x² + 4x + 1 = 0

2.- Complete the trinomial

                           x² + 4x        = -1

                           x² + 4x + (2)² = -1 + (2)²

                           (x + 2)² = -1 + 4

                           (x + 2)² = 3

                            x + 2 =± [tex]\sqrt{3}[/tex]

Solve for x

                        x₁ = -2 + [tex]\sqrt{3}[/tex]       and x₂ = -2 - [tex]\sqrt{3}[/tex]                

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