What are the solutions to the equation completesquare 3x^2+9x+5 ?

The solutions to the equation completesquare 3x^2+9x+5 are 3(x+3/2)^2-7/4

Find the zeros of completesquare 3x^2+9x+5

The zeros of completesquare 3x^2+9x+5 are 3(x+3/2)^2-7/4

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complete the square

3 x^{2} + 9 x + 5

3 (x + \frac{3}{2})^{2} - \frac{7}{4}

Solution steps

3 x^{2} + 9 x + 5

Write

3 x^{2} + 9 x + 5

in the form:

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

Factor out

3

3 (x^{2} + 3 x + \frac{5}{3})

2 a = 3 : a = \frac{3}{2}

Add and subtract

(\frac{3}{2})^{2}

3 (x^{2} + 3 x + \frac{5}{3} + (\frac{3}{2})^{2} - (\frac{3}{2})^{2})

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

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

3 ((x + \frac{3}{2})^{2} + \frac{5}{3} - (\frac{3}{2})^{2})

Simplify

3 (x + \frac{3}{2})^{2} - \frac{7}{4}

x, x^{2} + y^{2} + (z - 5)^{2} = 25

6 x^{2} - 16 = 0

2 r^{2} + 6 r + 4 = 0

(x - 6)^{2} = 100

x^{2} + \frac{14}{15} x + \frac{1}{5} = 0

What are the solutions to the equation completesquare 3x^2+9x+5 ?
The solutions to the equation completesquare 3x^2+9x+5 are 3(x+3/2)^2-7/4
Find the zeros of completesquare 3x^2+9x+5
The zeros of completesquare 3x^2+9x+5 are 3(x+3/2)^2-7/4