What are the solutions to the equation completesquare 7x^2+5x-8 ?

The solutions to the equation completesquare 7x^2+5x-8 are 7(x+5/14)^2-249/28

Find the zeros of completesquare 7x^2+5x-8

The zeros of completesquare 7x^2+5x-8 are 7(x+5/14)^2-249/28

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complete the square

7 x^{2} + 5 x - 8

7 (x + \frac{5}{14})^{2} - \frac{249}{28}

Solution steps

7 x^{2} + 5 x - 8

Write

7 x^{2} + 5 x - 8

in the form:

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

Factor out

7

7 (x^{2} + \frac{5 x}{7} - \frac{8}{7})

2 a = \frac{5}{7} : a = \frac{5}{14}

Add and subtract

(\frac{5}{14})^{2}

7 (x^{2} + \frac{5 x}{7} - \frac{8}{7} + (\frac{5}{14})^{2} - (\frac{5}{14})^{2})

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

x^{2} + \frac{5}{7} x + (\frac{5}{14})^{2} = (x + \frac{5}{14})^{2}

7 ((x + \frac{5}{14})^{2} - \frac{8}{7} - (\frac{5}{14})^{2})

Simplify

7 (x + \frac{5}{14})^{2} - \frac{249}{28}

- 2 x^{2} = 2

- 2 x^{2} = 6

(4 x - 6)^{2} = 12

4 x^{2} - 1.5 = 3.5

10 r^{2} - 2 r - 19 = 0

What are the solutions to the equation completesquare 7x^2+5x-8 ?
The solutions to the equation completesquare 7x^2+5x-8 are 7(x+5/14)^2-249/28
Find the zeros of completesquare 7x^2+5x-8
The zeros of completesquare 7x^2+5x-8 are 7(x+5/14)^2-249/28