What are the solutions to the equation completesquare 2x^2+5x+7 ?

The solutions to the equation completesquare 2x^2+5x+7 are 2(x+5/4)^2+31/8

Find the zeros of completesquare 2x^2+5x+7

The zeros of completesquare 2x^2+5x+7 are 2(x+5/4)^2+31/8

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complete the square

2 x^{2} + 5 x + 7

2 (x + \frac{5}{4})^{2} + \frac{31}{8}

Solution steps

2 x^{2} + 5 x + 7

Write

2 x^{2} + 5 x + 7

in the form:

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

Factor out

2

2 (x^{2} + \frac{5 x}{2} + \frac{7}{2})

2 a = \frac{5}{2} : a = \frac{5}{4}

Add and subtract

(\frac{5}{4})^{2}

2 (x^{2} + \frac{5 x}{2} + \frac{7}{2} + (\frac{5}{4})^{2} - (\frac{5}{4})^{2})

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

x^{2} + \frac{5}{2} x + (\frac{5}{4})^{2} = (x + \frac{5}{4})^{2}

2 ((x + \frac{5}{4})^{2} + \frac{7}{2} - (\frac{5}{4})^{2})

Simplify

2 (x + \frac{5}{4})^{2} + \frac{31}{8}

(x - 1) (x + 2) = 4

x^{2} + 8 = 89

x^{2} + 8 = 15

1 + 2 + 3 + n = \frac{1}{2} n (n + 1)

4 x^{2} + 20 x + 45 = 0

What are the solutions to the equation completesquare 2x^2+5x+7 ?
The solutions to the equation completesquare 2x^2+5x+7 are 2(x+5/4)^2+31/8
Find the zeros of completesquare 2x^2+5x+7
The zeros of completesquare 2x^2+5x+7 are 2(x+5/4)^2+31/8