What are the solutions to the equation completesquare 2x^2+6x-5 ?

The solutions to the equation completesquare 2x^2+6x-5 are 2(x+3/2)^2-19/2

Find the zeros of completesquare 2x^2+6x-5

The zeros of completesquare 2x^2+6x-5 are 2(x+3/2)^2-19/2

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complete the square

2 x^{2} + 6 x - 5

2 (x + \frac{3}{2})^{2} - \frac{19}{2}

Solution steps

2 x^{2} + 6 x - 5

Write

2 x^{2} + 6 x - 5

in the form:

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

Factor out

2

2 (x^{2} + 3 x - \frac{5}{2})

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

Add and subtract

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

2 (x^{2} + 3 x - \frac{5}{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{5}{2} - (\frac{3}{2})^{2})

Simplify

2 (x + \frac{3}{2})^{2} - \frac{19}{2}

2 x^{2} + 6 x + 5

3 r^{2} + 4 r + 7 = 0

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

x = \frac{x ^{2}}{4}

3 x^{2} + 6 = - 9 x

What are the solutions to the equation completesquare 2x^2+6x-5 ?
The solutions to the equation completesquare 2x^2+6x-5 are 2(x+3/2)^2-19/2
Find the zeros of completesquare 2x^2+6x-5
The zeros of completesquare 2x^2+6x-5 are 2(x+3/2)^2-19/2