What are the solutions to the equation completesquare 2x^2-x-3 ?

The solutions to the equation completesquare 2x^2-x-3 are 2(x-1/4)^2-25/8

Find the zeros of completesquare 2x^2-x-3

The zeros of completesquare 2x^2-x-3 are 2(x-1/4)^2-25/8

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complete the square

2 x^{2} - x - 3

2 (x - \frac{1}{4})^{2} - \frac{25}{8}

Solution steps

2 x^{2} - x - 3

Write

2 x^{2} - x - 3

in the form:

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

Factor out

2

2 (x^{2} - \frac{x}{2} - \frac{3}{2})

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

Add and subtract

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

2 (x^{2} - \frac{x}{2} - \frac{3}{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{3}{2} - (- \frac{1}{4})^{2})

Simplify

2 (x - \frac{1}{4})^{2} - \frac{25}{8}

2 x^{2} - x - 6

(2 x + 3)^{2} = 9

(x - 1) (2 x + 5) = 0

6 x (x - 2) - 3 = 2 (x - 2) (x + 2) - 4

7 - 0.0000003 x^{2} + 0.0006 x - 6 = 0

What are the solutions to the equation completesquare 2x^2-x-3 ?
The solutions to the equation completesquare 2x^2-x-3 are 2(x-1/4)^2-25/8
Find the zeros of completesquare 2x^2-x-3
The zeros of completesquare 2x^2-x-3 are 2(x-1/4)^2-25/8