What are the solutions to the equation completesquare-4x^2+2x+8 ?

The solutions to the equation completesquare-4x^2+2x+8 are -4(x-1/4)^2+33/4

Find the zeros of completesquare-4x^2+2x+8

The zeros of completesquare-4x^2+2x+8 are -4(x-1/4)^2+33/4

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complete the square

- 4 x^{2} + 2 x + 8

- 4 (x - \frac{1}{4})^{2} + \frac{33}{4}

Solution steps

- 4 x^{2} + 2 x + 8

Write

- 4 x^{2} + 2 x + 8

in the form:

x^{2} + 2 a x + a^{2}

Factor out

- 4

- 4 (x^{2} - \frac{x}{2} - 2)

2 a = - \frac{1}{2} : a = - \frac{1}{4}

Add and subtract

(- \frac{1}{4})^{2}

- 4 (x^{2} - \frac{x}{2} - 2 + (- \frac{1}{4})^{2} - (- \frac{1}{4})^{2})

x^{2} + 2 a x + a^{2} = (x + a)^{2}

x^{2} - \frac{1}{2} x + (- \frac{1}{4})^{2} = (x - \frac{1}{4})^{2}

- 4 ((x - \frac{1}{4})^{2} - 2 - (- \frac{1}{4})^{2})

Simplify

- 4 (x - \frac{1}{4})^{2} + \frac{33}{4}

5 x^{2} - 3 x - 0 = 0

0 = 4 x^{2} - 6

x^{2} - 15 x - 6 = 0

40.46 x^{2} - 200.4 x - 261 = 0

3 = 2 x^{2}

What are the solutions to the equation completesquare-4x^2+2x+8 ?
The solutions to the equation completesquare-4x^2+2x+8 are -4(x-1/4)^2+33/4
Find the zeros of completesquare-4x^2+2x+8
The zeros of completesquare-4x^2+2x+8 are -4(x-1/4)^2+33/4