Question

⅙x²+⅔x+⅓=0 using quadratic formula​

Answer 1

Step-by-step explanation:

multiply throughout by 6 to get rid of fraction

=> x² + 4x + 2 = 0

a = 1, b = 4 and c = 2

x = [-b ± √(b² - 4ac)] / 2a

=> x = [- 4 ± √( 4² - 4×1×2)] / 2

=> x = [- 4 ± √(16 - 8)] / 2

=> x = [- 4 ± √8] / 2

=> x = [- 4 ± 2√2] / 2

=> x = 2 [- 2 ± √2] /2

=> x = - 2 + √2 and x = - 2 - √2

Answer 2

$All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.$

$This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{1}{6}\approx 0.166666667 for a, \frac{2}{3}\approx 0.666666667 for b, and \frac{1}{3}\approx 0.333333333 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.$

$x=\frac{-\frac{2}{3}±\sqrt{\left(\frac{2}{3}\right)^{2}-4\times \left(\frac{1}{6}\right)\times \left(\frac{1}{3}\right)}}{2\times \left(\frac{1}{6}\right)}$

$Square \frac{2}{3}\approx 0.666666667 by squaring both the numerator and the denominator of the fraction.$

$x=\frac{-\frac{2}{3}±\sqrt{\frac{4}{9}-4\times \left(\frac{1}{6}\right)\times \left(\frac{1}{3}\right)}}{2\times \left(\frac{1}{6}\right)}$

$Multiply -4 times \frac{1}{6}\approx 0.166666667.$

$x=\frac{-\frac{2}{3}±\sqrt{\frac{4}{9}-\frac{2}{3}\times \left(\frac{1}{3}\right)}}{2\times \left(\frac{1}{6}\right)}$

$Multiply -\frac{2}{3}\approx -0.666666667 times \frac{1}{3}\approx 0.333333333 by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.$

$x=\frac{-\frac{2}{3}±\sqrt{\frac{4-2}{9}}}{2\times \left(\frac{1}{6}\right)}$

$Add \frac{4}{9}\approx 0.444444444 to -\frac{2}{9}\approx -0.222222222 by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.$

$Now solve the equation x=\frac{-\frac{2}{3}±\frac{\sqrt{2}}{3}}{\frac{1}{3}} when ± is plus. Add -\frac{2}{3}\approx -0.666666667 to \frac{\sqrt{2}}{3}\approx 0.471404521.$

$Divide \frac{-2-\sqrt{2}}{3}\approx -1.138071187 by \frac{1}{3}\approx 0.333333333 by multiplying \frac{-2-\sqrt{2}}{3}\approx -1.138071187 by the reciprocal of \frac{1}{3}\approx 0.333333333.$

$x=\sqrt{2}-2 x=-\sqrt{2}-2$