What are the solutions to the equation completesquare 4x^2+2x+5 ?

The solutions to the equation completesquare 4x^2+2x+5 are 4(x+1/4)^2+19/4

Find the zeros of completesquare 4x^2+2x+5

The zeros of completesquare 4x^2+2x+5 are 4(x+1/4)^2+19/4

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complete the square

4 x^{2} + 2 x + 5

4 (x + \frac{1}{4})^{2} + \frac{19}{4}

Solution steps

4 x^{2} + 2 x + 5

Write

4 x^{2} + 2 x + 5

in the form:

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

Factor out

4

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

2 a = \frac{1}{2} : a = \frac{1}{4}

Add and subtract

(\frac{1}{4})^{2}

4 (x^{2} + \frac{x}{2} + \frac{5}{4} + (\frac{1}{4})^{2} - (\frac{1}{4})^{2})

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

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

4 ((x + \frac{1}{4})^{2} + \frac{5}{4} - (\frac{1}{4})^{2})

Simplify

4 (x + \frac{1}{4})^{2} + \frac{19}{4}

4.9 x^{2} - 90 x - 150 = 0

5 x^{2} + 31623 x + 50 = 0

- 4.9 t^{2} + 18 t + 7.4 = 0

4 (x + 5)^{2} + 6 = 54

- 4 x^{2} - 4 x = 0

What are the solutions to the equation completesquare 4x^2+2x+5 ?
The solutions to the equation completesquare 4x^2+2x+5 are 4(x+1/4)^2+19/4
Find the zeros of completesquare 4x^2+2x+5
The zeros of completesquare 4x^2+2x+5 are 4(x+1/4)^2+19/4