What are the solutions to the equation completesquare 2x^2-4x+5 ?

The solutions to the equation completesquare 2x^2-4x+5 are 2(x-1)^2+3

Find the zeros of completesquare 2x^2-4x+5

The zeros of completesquare 2x^2-4x+5 are 2(x-1)^2+3

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complete the square

2 x^{2} - 4 x + 5

2 (x - 1)^{2} + 3

Solution steps

2 x^{2} - 4 x + 5

Write

2 x^{2} - 4 x + 5

in the form:

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

Factor out

2

2 (x^{2} - 2 x + \frac{5}{2})

2 a = - 2 : a = - 1

Add and subtract

(- 1)^{2}

2 (x^{2} - 2 x + \frac{5}{2} + (- 1)^{2} - (- 1)^{2})

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

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

2 ((x - 1)^{2} + \frac{5}{2} - (- 1)^{2})

Simplify

2 (x - 1)^{2} + 3

x^{2} + 4 x = x + 10

x^{2} + 5 x + 9 = 0

x^{2} + 6 x + 13

x^{2} + 17 = 0

4 x^{2} + 9 = 105

What are the solutions to the equation completesquare 2x^2-4x+5 ?
The solutions to the equation completesquare 2x^2-4x+5 are 2(x-1)^2+3
Find the zeros of completesquare 2x^2-4x+5
The zeros of completesquare 2x^2-4x+5 are 2(x-1)^2+3