What are the solutions to the equation completesquare 4x^2-6x+3 ?

The solutions to the equation completesquare 4x^2-6x+3 are 4(x-3/4)^2+3/4

Find the zeros of completesquare 4x^2-6x+3

The zeros of completesquare 4x^2-6x+3 are 4(x-3/4)^2+3/4

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complete the square

4 x^{2} - 6 x + 3

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

Solution steps

4 x^{2} - 6 x + 3

Write

4 x^{2} - 6 x + 3

in the form:

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

Factor out

4

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

2 a = - \frac{3}{2} : a = - \frac{3}{4}

Add and subtract

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

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

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

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

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

Simplify

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

2 x^{2} + 10 x - 1092 = 0

x^{2} - 31 x - 180 = 0

(x + 6)^{2} - 49 = 0

(x) = 2 x^{2} - 7 x - 4

3 y^{2} + 16 y + 5 = 0

What are the solutions to the equation completesquare 4x^2-6x+3 ?
The solutions to the equation completesquare 4x^2-6x+3 are 4(x-3/4)^2+3/4
Find the zeros of completesquare 4x^2-6x+3
The zeros of completesquare 4x^2-6x+3 are 4(x-3/4)^2+3/4