What are the solutions to the equation completesquare-4x^2+4x+3 ?

The solutions to the equation completesquare-4x^2+4x+3 are -4(x-1/2)^2+4

Find the zeros of completesquare-4x^2+4x+3

The zeros of completesquare-4x^2+4x+3 are -4(x-1/2)^2+4

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complete the square

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

- 4 (x - \frac{1}{2})^{2} + 4

Solution steps

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

Write

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

in the form:

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

Factor out

- 4

- 4 (x^{2} - x - \frac{3}{4})

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

Add and subtract

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

- 4 (x^{2} - x - \frac{3}{4} + (- \frac{1}{2})^{2} - (- \frac{1}{2})^{2})

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

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

- 4 ((x - \frac{1}{2})^{2} - \frac{3}{4} - (- \frac{1}{2})^{2})

Simplify

- 4 (x - \frac{1}{2})^{2} + 4

(x + 3) (x + 2) = 0

\frac{2}{5} x^{2} = 0

3 x^{2} + 6 x - 15 = 0

x^{2} + 12 x + 8 = - 5

4 x^{2} + 22 x + 30 = 0

What are the solutions to the equation completesquare-4x^2+4x+3 ?
The solutions to the equation completesquare-4x^2+4x+3 are -4(x-1/2)^2+4
Find the zeros of completesquare-4x^2+4x+3
The zeros of completesquare-4x^2+4x+3 are -4(x-1/2)^2+4