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

The solutions to the equation completesquare 2x^2-x-2 are 2(x-1/4)^2-17/8

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

The zeros of completesquare 2x^2-x-2 are 2(x-1/4)^2-17/8

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complete the square

2 x^{2} - x - 2

2 (x - \frac{1}{4})^{2} - \frac{17}{8}

Solution steps

2 x^{2} - x - 2

Write

2 x^{2} - x - 2

in the form:

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

Factor out

2

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

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

Add and subtract

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

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

Simplify

2 (x - \frac{1}{4})^{2} - \frac{17}{8}

(2 x + 3)^{2} = 4

x^{2} + 4 x + 4 = 2 x + 7

t, f = k t^{2} + 2

25 x^{2} + 30 x = - 5

5 (8) = x (6 + x)

What are the solutions to the equation completesquare 2x^2-x-2 ?
The solutions to the equation completesquare 2x^2-x-2 are 2(x-1/4)^2-17/8
Find the zeros of completesquare 2x^2-x-2
The zeros of completesquare 2x^2-x-2 are 2(x-1/4)^2-17/8