What are the solutions to the equation completesquare 5x^2+9x+1 ?

The solutions to the equation completesquare 5x^2+9x+1 are 5(x+9/10)^2-61/20

Find the zeros of completesquare 5x^2+9x+1

The zeros of completesquare 5x^2+9x+1 are 5(x+9/10)^2-61/20

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complete the square

5 x^{2} + 9 x + 1

5 (x + \frac{9}{10})^{2} - \frac{61}{20}

Solution steps

5 x^{2} + 9 x + 1

Write

5 x^{2} + 9 x + 1

in the form:

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

Factor out

5

5 (x^{2} + \frac{9 x}{5} + \frac{1}{5})

2 a = \frac{9}{5} : a = \frac{9}{10}

Add and subtract

(\frac{9}{10})^{2}

5 (x^{2} + \frac{9 x}{5} + \frac{1}{5} + (\frac{9}{10})^{2} - (\frac{9}{10})^{2})

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

x^{2} + \frac{9}{5} x + (\frac{9}{10})^{2} = (x + \frac{9}{10})^{2}

5 ((x + \frac{9}{10})^{2} + \frac{1}{5} - (\frac{9}{10})^{2})

Simplify

5 (x + \frac{9}{10})^{2} - \frac{61}{20}

x^{2} - 8 x + 12 = 0

a, y = a^{2}

2 m^{2} - 5 m - 3 = 0

y^{2} - 4 y + 1 = 0

x^{2} + 20 x + 109 = 0

What are the solutions to the equation completesquare 5x^2+9x+1 ?
The solutions to the equation completesquare 5x^2+9x+1 are 5(x+9/10)^2-61/20
Find the zeros of completesquare 5x^2+9x+1
The zeros of completesquare 5x^2+9x+1 are 5(x+9/10)^2-61/20