What are the solutions to the equation completesquare 2x^2-6x+11 ?

The solutions to the equation completesquare 2x^2-6x+11 are 2(x-3/2)^2+13/2

Find the zeros of completesquare 2x^2-6x+11

The zeros of completesquare 2x^2-6x+11 are 2(x-3/2)^2+13/2

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complete the square

2 x^{2} - 6 x + 11

2 (x - \frac{3}{2})^{2} + \frac{13}{2}

Solution steps

2 x^{2} - 6 x + 11

Write

2 x^{2} - 6 x + 11

in the form:

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

Factor out

2

2 (x^{2} - 3 x + \frac{11}{2})

2 a = - 3 : a = - \frac{3}{2}

Add and subtract

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

2 (x^{2} - 3 x + \frac{11}{2} + (- \frac{3}{2})^{2} - (- \frac{3}{2})^{2})

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

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

2 ((x - \frac{3}{2})^{2} + \frac{11}{2} - (- \frac{3}{2})^{2})

Simplify

2 (x - \frac{3}{2})^{2} + \frac{13}{2}

1 = x^{2} + 2 x

6 x^{2} + 4 = - 17 x + 7

2 x^{2} - 15 = - x^{2} + 12

y, (x + y)^{2} = 2 x y

2 c^{2} + 12 c + 11 = 0

What are the solutions to the equation completesquare 2x^2-6x+11 ?
The solutions to the equation completesquare 2x^2-6x+11 are 2(x-3/2)^2+13/2
Find the zeros of completesquare 2x^2-6x+11
The zeros of completesquare 2x^2-6x+11 are 2(x-3/2)^2+13/2