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

The solutions to the equation completesquare-2x^2+x-1 are -2(x-1/4)^2-7/8

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

The zeros of completesquare-2x^2+x-1 are -2(x-1/4)^2-7/8

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complete the square

- 2 x^{2} + x - 1

- 2 (x - \frac{1}{4})^{2} - \frac{7}{8}

Solution steps

- 2 x^{2} + x - 1

Write

- 2 x^{2} + x - 1

in the form:

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

Factor out

- 2

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

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

Add and subtract

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

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

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

Simplify

- 2 (x - \frac{1}{4})^{2} - \frac{7}{8}

X^{2} + 2 X = 0

- 7 + 16 k^{2} = 9

(x + 2) (x - 4) = 27

2 x^{2} + 3 x - 1

x^{2} + 3 x + 2 = 1

What are the solutions to the equation completesquare-2x^2+x-1 ?
The solutions to the equation completesquare-2x^2+x-1 are -2(x-1/4)^2-7/8
Find the zeros of completesquare-2x^2+x-1
The zeros of completesquare-2x^2+x-1 are -2(x-1/4)^2-7/8