How do you solve $3 x^{2} + 5 x = 2$ $3x^2+5x=2$ by completing the square?

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How do you solve $3 x^{2} + 5 x = 2$ $3x^2+5x=2$ by completing the square?

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Answer 1 · 2018-06-26T10:15:03

$x = - 2, \frac{1}{3}$ $color(violet)(x = -2, 1/3$

Explanation:

$3 x^{2} + 5 x = 2$ $3x^2 + 5x = 2$

${(\sqrt{3 x})}^{2} + 2 \cdot \sqrt{3} \cdot x \cdot (\frac{5}{2 \cdot \sqrt{3}}) = 2$ $(sqrt(3x))^2 + 2 * sqrt3 * x * (5/ (2 *sqrt3)) = 2$

${(\sqrt{3} x)}^{2} + 2 \cdot \sqrt{3} \cdot x \cdot (\frac{5}{2 \cdot \sqrt{3}}) + {(\frac{5}{2 \sqrt{3}})}^{2} = 2 + {(\frac{5}{2 \sqrt{3}})}^{2}$ $(sqrt3 x)^2 + 2 * sqrt3 * x * (5/ (2 *sqrt3)) + (5/(2 sqrt3))^2 = 2 + (5/(2 sqrt3))^2$

${((\sqrt{3} x) + \frac{5}{2 \sqrt{3}})}^{2} = 2 + \frac{25}{12} = \frac{49}{12}$ $((sqrt3 x) + 5/(2 sqrt3))^2 = 2 + 25/12 = 49/12$

${((\sqrt{3} x) + \frac{5}{2 \sqrt{3}})}^{2} = {(\sqrt{\frac{49}{12}})}^{2}$ $((sqrt3 x) + 5/(2 sqrt3))^2 = (sqrt(49/12))^2$

$\sqrt{3} x + \frac{5}{2 \sqrt{3}} = \pm \frac{7}{2 \sqrt{3}}$ $sqrt 3 x + 5/ (2 sqrt3) = +- 7/ (2 sqrt3)$

$\sqrt{3} x = \frac{- 5 \pm 7}{2 \sqrt{3}}$ $sqrt3 x = (-5 +- 7) / (2 sqrt3)$

$x = \frac{- 5 \pm 7}{6} = - 2, \frac{1}{3}$ $x = (-5 +- 7) / 6 = -2, 1/3$

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