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

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

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

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

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complete the square

4 x^{2} + 6 x

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

Solution steps

4 x^{2} + 6 x

Write

4 x^{2} + 6 x

in the form:

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

Factor out

4

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

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})^{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})^{2})

Simplify

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

2 (t - 3)^{2} - 72 = 0

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

5 x^{2} - 10 x - 255 = 0

8 x^{2} - x - 9 = 0

x^{2} - 5 x + \frac{9}{4} = 0

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