What are the solutions to the equation completesquare 10x^2-3x+1 ?

The solutions to the equation completesquare 10x^2-3x+1 are 10(x-3/20)^2+31/40

Find the zeros of completesquare 10x^2-3x+1

The zeros of completesquare 10x^2-3x+1 are 10(x-3/20)^2+31/40

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complete the square

10 x^{2} - 3 x + 1

10 (x - \frac{3}{20})^{2} + \frac{31}{40}

Solution steps

10 x^{2} - 3 x + 1

Write

10 x^{2} - 3 x + 1

in the form:

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

Factor out

10

10 (x^{2} - \frac{3 x}{10} + \frac{1}{10})

2 a = - \frac{3}{10} : a = - \frac{3}{20}

Add and subtract

(- \frac{3}{20})^{2}

10 (x^{2} - \frac{3 x}{10} + \frac{1}{10} + (- \frac{3}{20})^{2} - (- \frac{3}{20})^{2})

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

x^{2} - \frac{3}{10} x + (- \frac{3}{20})^{2} = (x - \frac{3}{20})^{2}

10 ((x - \frac{3}{20})^{2} + \frac{1}{10} - (- \frac{3}{20})^{2})

Simplify

10 (x - \frac{3}{20})^{2} + \frac{31}{40}

(2 x + 7)^{2} = 48

2 x^{2} - 15 x - 27 = 0

x, y = 5 x - x^{2}

x, x^{2} + 9 x + 20 = 0

9 x^{2} = 2 x

What are the solutions to the equation completesquare 10x^2-3x+1 ?
The solutions to the equation completesquare 10x^2-3x+1 are 10(x-3/20)^2+31/40
Find the zeros of completesquare 10x^2-3x+1
The zeros of completesquare 10x^2-3x+1 are 10(x-3/20)^2+31/40