What are the solutions to the equation completesquare-9x^2+6x+15 ?

The solutions to the equation completesquare-9x^2+6x+15 are -9(x-1/3)^2+16

Find the zeros of completesquare-9x^2+6x+15

The zeros of completesquare-9x^2+6x+15 are -9(x-1/3)^2+16

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complete the square

- 9 x^{2} + 6 x + 15

- 9 (x - \frac{1}{3})^{2} + 16

Solution steps

- 9 x^{2} + 6 x + 15

Write

- 9 x^{2} + 6 x + 15

in the form:

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

Factor out

- 9

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

2 a = - \frac{2}{3} : a = - \frac{1}{3}

Add and subtract

(- \frac{1}{3})^{2}

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

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

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

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

Simplify

- 9 (x - \frac{1}{3})^{2} + 16

(x + 6)^{2} = 1

z^{2} - 8 z

4 x + 4 x^{2} = - 1

(x - 3)^{2} + 2 = 18

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

What are the solutions to the equation completesquare-9x^2+6x+15 ?
The solutions to the equation completesquare-9x^2+6x+15 are -9(x-1/3)^2+16
Find the zeros of completesquare-9x^2+6x+15
The zeros of completesquare-9x^2+6x+15 are -9(x-1/3)^2+16