What are the solutions to the equation completesquare 4x^2-6x+9 ?

The solutions to the equation completesquare 4x^2-6x+9 are 4(x-3/4)^2+27/4

Find the zeros of completesquare 4x^2-6x+9

The zeros of completesquare 4x^2-6x+9 are 4(x-3/4)^2+27/4

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complete the square

4 x^{2} - 6 x + 9

4 (x - \frac{3}{4})^{2} + \frac{27}{4}

Solution steps

4 x^{2} - 6 x + 9

Write

4 x^{2} - 6 x + 9

in the form:

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

Factor out

4

4 (x^{2} - \frac{3 x}{2} + \frac{9}{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{9}{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{9}{4} - (- \frac{3}{4})^{2})

Simplify

4 (x - \frac{3}{4})^{2} + \frac{27}{4}

2 r^{2} + 8 r - 19 = 0

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

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

2 x^{2} - 8 = 41

3 x^{2} - x - 48 = 0

What are the solutions to the equation completesquare 4x^2-6x+9 ?
The solutions to the equation completesquare 4x^2-6x+9 are 4(x-3/4)^2+27/4
Find the zeros of completesquare 4x^2-6x+9
The zeros of completesquare 4x^2-6x+9 are 4(x-3/4)^2+27/4