What are the solutions to the equation completesquare 5x^2+2x-3 ?

The solutions to the equation completesquare 5x^2+2x-3 are 5(x+1/5)^2-16/5

Find the zeros of completesquare 5x^2+2x-3

The zeros of completesquare 5x^2+2x-3 are 5(x+1/5)^2-16/5

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complete the square

5 x^{2} + 2 x - 3

5 (x + \frac{1}{5})^{2} - \frac{16}{5}

Solution steps

5 x^{2} + 2 x - 3

Write

5 x^{2} + 2 x - 3

in the form:

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

Factor out

5

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

2 a = \frac{2}{5} : a = \frac{1}{5}

Add and subtract

(\frac{1}{5})^{2}

5 (x^{2} + \frac{2 x}{5} - \frac{3}{5} + (\frac{1}{5})^{2} - (\frac{1}{5})^{2})

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

x^{2} + \frac{2}{5} x + (\frac{1}{5})^{2} = (x + \frac{1}{5})^{2}

5 ((x + \frac{1}{5})^{2} - \frac{3}{5} - (\frac{1}{5})^{2})

Simplify

5 (x + \frac{1}{5})^{2} - \frac{16}{5}

r^{2} - r - 14 = 2 r

14 x^{2} - 36 x + 16 = 0

2 x^{2} + 36 x + 34 = 0

x^{2} = x + 90

- 6 x + 3 x^{2} = 0

What are the solutions to the equation completesquare 5x^2+2x-3 ?
The solutions to the equation completesquare 5x^2+2x-3 are 5(x+1/5)^2-16/5
Find the zeros of completesquare 5x^2+2x-3
The zeros of completesquare 5x^2+2x-3 are 5(x+1/5)^2-16/5