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

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

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

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

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complete the square

2 x^{2} - 2 x + 1

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

Solution steps

2 x^{2} - 2 x + 1

Write

2 x^{2} - 2 x + 1

in the form:

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

Factor out

2

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

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

Add and subtract

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

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

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

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

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

Simplify

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

- 26 = - x^{2} - 1

9 (x^{2} + 1) = 34

\frac{x ^{2}}{2} = 7 x

x^{2} - 3 x + (- \frac{9}{4}) = 12

x^{2} - 16 x - 64 = 0

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