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

The solutions to the equation completesquare 2x^2-7x+5 are 2(x-7/4)^2-9/8

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

The zeros of completesquare 2x^2-7x+5 are 2(x-7/4)^2-9/8

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complete the square

2 x^{2} - 7 x + 5

2 (x - \frac{7}{4})^{2} - \frac{9}{8}

Solution steps

2 x^{2} - 7 x + 5

Write

2 x^{2} - 7 x + 5

in the form:

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

Factor out

2

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

2 a = - \frac{7}{2} : a = - \frac{7}{4}

Add and subtract

(- \frac{7}{4})^{2}

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

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

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

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

Simplify

2 (x - \frac{7}{4})^{2} - \frac{9}{8}

12 x^{2} - 30 x = 0

4 x^{2} - 1 = 15

n^{2} - 20 n + 100 = 40

a = 4 π r^{2}

x^{2} - \frac{2}{5} x - 7

What are the solutions to the equation completesquare 2x^2-7x+5 ?
The solutions to the equation completesquare 2x^2-7x+5 are 2(x-7/4)^2-9/8
Find the zeros of completesquare 2x^2-7x+5
The zeros of completesquare 2x^2-7x+5 are 2(x-7/4)^2-9/8