What are the solutions to the equation completesquare 4+12x-2x^2 ?

The solutions to the equation completesquare 4+12x-2x^2 are -2(x-3)^2+22

Find the zeros of completesquare 4+12x-2x^2

The zeros of completesquare 4+12x-2x^2 are -2(x-3)^2+22

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complete the square

4 + 12 x - 2 x^{2}

- 2 (x - 3)^{2} + 22

Solution steps

4 + 12 x - 2 x^{2}

Write in the standard form

a x^{2} + b x + c

- 2 x^{2} + 12 x + 4

Write

- 2 x^{2} + 12 x + 4

in the form:

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

Factor out

- 2

- 2 (x^{2} - 6 x - 2)

2 a = - 6 : a = - 3

Add and subtract

(- 3)^{2}

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

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

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

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

Simplify

- 2 (x - 3)^{2} + 22

4 x^{2} + 2 x - 7 = - 3 x^{2} - 2

- 3 x^{2} - 4 x + 15 = 0

3 x^{2} - 6 x - 189 = 0

4 y^{2} - 49 = 0

y, x^{3} y + y^{2} - x^{2} = 5

What are the solutions to the equation completesquare 4+12x-2x^2 ?
The solutions to the equation completesquare 4+12x-2x^2 are -2(x-3)^2+22
Find the zeros of completesquare 4+12x-2x^2
The zeros of completesquare 4+12x-2x^2 are -2(x-3)^2+22