What are the solutions to the equation completesquare-7/2 x^2+3x+8/3 ?

The solutions to the equation completesquare-7/2 x^2+3x+8/3 are -7/2 (x-3/7)^2+139/42

Find the zeros of completesquare-7/2 x^2+3x+8/3

The zeros of completesquare-7/2 x^2+3x+8/3 are -7/2 (x-3/7)^2+139/42

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complete the square

- \frac{7}{2} x^{2} + 3 x + \frac{8}{3}

- \frac{7}{2} (x - \frac{3}{7})^{2} + \frac{139}{42}

Solution steps

- \frac{7}{2} x^{2} + 3 x + \frac{8}{3}

Write in the standard form

a x^{2} + b x + c

- \frac{7 x ^{2}}{2} + 3 x + \frac{8}{3}

Write

- \frac{7 x ^{2}}{2} + 3 x + \frac{8}{3}

in the form:

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

Factor out

- \frac{7}{2}

- \frac{7}{2} (x^{2} - \frac{6 x}{7} - \frac{16}{21})

2 a = - \frac{6}{7} : a = - \frac{3}{7}

Add and subtract

(- \frac{3}{7})^{2}

- \frac{7}{2} (x^{2} - \frac{6 x}{7} - \frac{16}{21} + (- \frac{3}{7})^{2} - (- \frac{3}{7})^{2})

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

x^{2} - \frac{6}{7} x + (- \frac{3}{7})^{2} = (x - \frac{3}{7})^{2}

- \frac{7}{2} ((x - \frac{3}{7})^{2} - \frac{16}{21} - (- \frac{3}{7})^{2})

Simplify

- \frac{7}{2} (x - \frac{3}{7})^{2} + \frac{139}{42}

(x + 1)^{2} + 2 x = 3 x (x + 1) + 5

(x - 3)^{2} + (x - 1)^{2} = 0

x^{2} + 4 x - 17 = 0

3 x^{2} + 42 x + 105 = 0

9 x^{2} - 10 x = x^{2} + 4 x

What are the solutions to the equation completesquare-7/2 x^2+3x+8/3 ?
The solutions to the equation completesquare-7/2 x^2+3x+8/3 are -7/2 (x-3/7)^2+139/42
Find the zeros of completesquare-7/2 x^2+3x+8/3
The zeros of completesquare-7/2 x^2+3x+8/3 are -7/2 (x-3/7)^2+139/42