What are the solutions to the equation completesquare 8x^2-x-1 ?

The solutions to the equation completesquare 8x^2-x-1 are 8(x-1/16)^2-33/32

Find the zeros of completesquare 8x^2-x-1

The zeros of completesquare 8x^2-x-1 are 8(x-1/16)^2-33/32

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complete the square

8 x^{2} - x - 1

8 (x - \frac{1}{16})^{2} - \frac{33}{32}

Solution steps

8 x^{2} - x - 1

Write

8 x^{2} - x - 1

in the form:

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

Factor out

8

8 (x^{2} - \frac{x}{8} - \frac{1}{8})

2 a = - \frac{1}{8} : a = - \frac{1}{16}

Add and subtract

(- \frac{1}{16})^{2}

8 (x^{2} - \frac{x}{8} - \frac{1}{8} + (- \frac{1}{16})^{2} - (- \frac{1}{16})^{2})

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

x^{2} - \frac{1}{8} x + (- \frac{1}{16})^{2} = (x - \frac{1}{16})^{2}

8 ((x - \frac{1}{16})^{2} - \frac{1}{8} - (- \frac{1}{16})^{2})

Simplify

8 (x - \frac{1}{16})^{2} - \frac{33}{32}

4 x^{2} + 32 x + 16 = 0

2 x^{2} - 4 x = - 6

(2 s - 1)^{2} - 255 = 0

13 x^{2} - x = 0

(r - 4) (r + 8) = - 24

What are the solutions to the equation completesquare 8x^2-x-1 ?
The solutions to the equation completesquare 8x^2-x-1 are 8(x-1/16)^2-33/32
Find the zeros of completesquare 8x^2-x-1
The zeros of completesquare 8x^2-x-1 are 8(x-1/16)^2-33/32