Expert Answer to "For Exercise, solve the equations and inequalities. Write..."

slaggingV

Answered question

2021-09-21

For Exercise, solve the equations and inequalities. Write the solution sets to the inequalities in interval notation.

3 x (x - 1) = x + 6

Obiajulu

Skilled2021-09-22Added 98 answers

Concept used:
Quadratic Formula

a x^{2} + b x + c = 0

x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}

Now, Solving the equation

3 x (x - 1) = x + 6

3 x^{2} - 3 x = x + 6

3 x^{2} - 3 x - x - 6 = 0

3 x^{2} - 4 x - 6 = 0

Now

x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}

Here,

a = 3, b = - 4, c = - 6

Then,

x = \frac{- (- 4) \pm \sqrt{{(- 4)}^{2} - 4 \times 3 \times (- 6)}}{2 \times 3}

x = \frac{4 \pm \sqrt{16 + 72}}{6}

x = \frac{4 \pm \sqrt{88}}{6}

x = \frac{4 \pm 2 \sqrt{22}}{6}

x = \frac{2 \pm \sqrt{22}}{3}

Answer: Hence, the values of x are

x = \frac{2 + \sqrt{22}}{3}

and

x = \frac{2 - \sqrt{22}}{3}

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