What are the solutions to the equation completesquare 4x^2+20x+25 ?

The solutions to the equation completesquare 4x^2+20x+25 are 4(x+5/2)^2

Find the zeros of completesquare 4x^2+20x+25

The zeros of completesquare 4x^2+20x+25 are 4(x+5/2)^2

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complete the square

4 x^{2} + 20 x + 25

4 (x + \frac{5}{2})^{2}

Solution steps

4 x^{2} + 20 x + 25

Write

4 x^{2} + 20 x + 25

in the form:

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

Factor out

4

4 (x^{2} + 5 x + \frac{25}{4})

2 a = 5 : a = \frac{5}{2}

Add and subtract

(\frac{5}{2})^{2}

4 (x^{2} + 5 x + \frac{25}{4} + (\frac{5}{2})^{2} - (\frac{5}{2})^{2})

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

x^{2} + 5 x + (\frac{5}{2})^{2} = (x + \frac{5}{2})^{2}

4 ((x + \frac{5}{2})^{2} + \frac{25}{4} - (\frac{5}{2})^{2})

Simplify

4 (x + \frac{5}{2})^{2}

- 5 x^{2} - 30 x + 95 = 0

8 x (x + 1) + (5 x - 1) (3 x + 5) = 3 (x + 1) (3 x + 5)

x, x^{2} y + y = 5

12 - x^{2} = 0

3 x^{2} - 5 x = 28

What are the solutions to the equation completesquare 4x^2+20x+25 ?
The solutions to the equation completesquare 4x^2+20x+25 are 4(x+5/2)^2
Find the zeros of completesquare 4x^2+20x+25
The zeros of completesquare 4x^2+20x+25 are 4(x+5/2)^2