What are the solutions to the equation completesquare 20x^2-24x+65 ?

The solutions to the equation completesquare 20x^2-24x+65 are 20(x-3/5)^2+289/5

Find the zeros of completesquare 20x^2-24x+65

The zeros of completesquare 20x^2-24x+65 are 20(x-3/5)^2+289/5

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complete the square

20 x^{2} - 24 x + 65

20 (x - \frac{3}{5})^{2} + \frac{289}{5}

Solution steps

20 x^{2} - 24 x + 65

Write

20 x^{2} - 24 x + 65

in the form:

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

Factor out

20

20 (x^{2} - \frac{6 x}{5} + \frac{13}{4})

2 a = - \frac{6}{5} : a = - \frac{3}{5}

Add and subtract

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

20 (x^{2} - \frac{6 x}{5} + \frac{13}{4} + (- \frac{3}{5})^{2} - (- \frac{3}{5})^{2})

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

x^{2} - \frac{6}{5} x + (- \frac{3}{5})^{2} = (x - \frac{3}{5})^{2}

20 ((x - \frac{3}{5})^{2} + \frac{13}{4} - (- \frac{3}{5})^{2})

Simplify

20 (x - \frac{3}{5})^{2} + \frac{289}{5}

(6 x - 7)^{2} = - 25

6 x^{2} + 10 x + 3 = 0

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

y^{2} - 3 = 0

3 (x - 2)^{2} = 21

What are the solutions to the equation completesquare 20x^2-24x+65 ?
The solutions to the equation completesquare 20x^2-24x+65 are 20(x-3/5)^2+289/5
Find the zeros of completesquare 20x^2-24x+65
The zeros of completesquare 20x^2-24x+65 are 20(x-3/5)^2+289/5