What are the solutions to the equation completesquare 5a^2-17a+1 ?

The solutions to the equation completesquare 5a^2-17a+1 are 5(a-17/10)^2-269/20

Find the zeros of completesquare 5a^2-17a+1

The zeros of completesquare 5a^2-17a+1 are 5(a-17/10)^2-269/20

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complete the square

5 a^{2} - 17 a + 1

5 (a - \frac{17}{10})^{2} - \frac{269}{20}

Solution steps

5 a^{2} - 17 a + 1

Write

5 a^{2} - 17 a + 1

in the form:

x^{2} + 2 b x + b^{2}

Factor out

5

5 (a^{2} - \frac{17 a}{5} + \frac{1}{5})

2 b = - \frac{17}{5} : b = - \frac{17}{10}

Add and subtract

(- \frac{17}{10})^{2}

5 (a^{2} - \frac{17 a}{5} + \frac{1}{5} + (- \frac{17}{10})^{2} - (- \frac{17}{10})^{2})

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

a^{2} - \frac{17}{5} a + (- \frac{17}{10})^{2} = (a - \frac{17}{10})^{2}

5 ((a - \frac{17}{10})^{2} + \frac{1}{5} - (- \frac{17}{10})^{2})

Simplify

5 (a - \frac{17}{10})^{2} - \frac{269}{20}

5 x^{2} - 7 x - 1 = 2 x

x^{2} + 26 x = 16

d^{2} - 6 d - 475 = 0

2 x^{2} - 6 x + 7 = 10.5

9 x^{2} + 5 x = 12 + 6 x + 3 x^{2}

What are the solutions to the equation completesquare 5a^2-17a+1 ?
The solutions to the equation completesquare 5a^2-17a+1 are 5(a-17/10)^2-269/20
Find the zeros of completesquare 5a^2-17a+1
The zeros of completesquare 5a^2-17a+1 are 5(a-17/10)^2-269/20