What are the solutions to the equation completesquare 3x^2-18x+15 ?

The solutions to the equation completesquare 3x^2-18x+15 are 3(x-3)^2-12

Find the zeros of completesquare 3x^2-18x+15

The zeros of completesquare 3x^2-18x+15 are 3(x-3)^2-12

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complete the square

3 x^{2} - 18 x + 15

3 (x - 3)^{2} - 12

Solution steps

3 x^{2} - 18 x + 15

Write

3 x^{2} - 18 x + 15

in the form:

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

Factor out

3

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

2 a = - 6 : a = - 3

Add and subtract

(- 3)^{2}

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

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

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

3 ((x - 3)^{2} + 5 - (- 3)^{2})

Simplify

3 (x - 3)^{2} - 12

- 3 (2 x - 1) (2 x + 1) = 2

6 - 7 x^{2} = 7

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

n^{2} + 5 n + 7 = 7

x, 5 x^{2} + 2 y^{2} = 0

What are the solutions to the equation completesquare 3x^2-18x+15 ?
The solutions to the equation completesquare 3x^2-18x+15 are 3(x-3)^2-12
Find the zeros of completesquare 3x^2-18x+15
The zeros of completesquare 3x^2-18x+15 are 3(x-3)^2-12