What are the solutions to the equation completesquare 2x^2+6x-1 ?

The solutions to the equation completesquare 2x^2+6x-1 are 2(x+3/2)^2-11/2

Find the zeros of completesquare 2x^2+6x-1

The zeros of completesquare 2x^2+6x-1 are 2(x+3/2)^2-11/2

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complete the square

2 x^{2} + 6 x - 1

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

Solution steps

2 x^{2} + 6 x - 1

Write

2 x^{2} + 6 x - 1

in the form:

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

Factor out

2

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

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

Add and subtract

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

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

Simplify

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

x^{2} + 2 x - 44 = 0

- 2 x^{2} = - 42

7 x^{2} + 14 x - 56 = 0

x^{2} = \frac{64}{81}

(2 x - 3)^{2} + 1 = 19

What are the solutions to the equation completesquare 2x^2+6x-1 ?
The solutions to the equation completesquare 2x^2+6x-1 are 2(x+3/2)^2-11/2
Find the zeros of completesquare 2x^2+6x-1
The zeros of completesquare 2x^2+6x-1 are 2(x+3/2)^2-11/2