What are the solutions to the equation completesquare-3x^2+6x+21 ?

The solutions to the equation completesquare-3x^2+6x+21 are -3(x-1)^2+24

Find the zeros of completesquare-3x^2+6x+21

The zeros of completesquare-3x^2+6x+21 are -3(x-1)^2+24

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complete the square

- 3 x^{2} + 6 x + 21

- 3 (x - 1)^{2} + 24

Solution steps

- 3 x^{2} + 6 x + 21

Write

- 3 x^{2} + 6 x + 21

in the form:

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

Factor out

- 3

- 3 (x^{2} - 2 x - 7)

2 a = - 2 : a = - 1

Add and subtract

(- 1)^{2}

- 3 (x^{2} - 2 x - 7 + (- 1)^{2} - (- 1)^{2})

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

x^{2} - 2 x + (- 1)^{2} = (x - 1)^{2}

- 3 ((x - 1)^{2} - 7 - (- 1)^{2})

Simplify

- 3 (x - 1)^{2} + 24

x^{2} = 768

2 x^{2} - 42 = 0

112 = - 16 x^{2} + 128 x

- 49 p^{2} = 7

- 2 x + x^{2} + \frac{3}{4} = 0

What are the solutions to the equation completesquare-3x^2+6x+21 ?
The solutions to the equation completesquare-3x^2+6x+21 are -3(x-1)^2+24
Find the zeros of completesquare-3x^2+6x+21
The zeros of completesquare-3x^2+6x+21 are -3(x-1)^2+24