Solve x ^ 2 + 1/6 * x - 2

Question

Factor the expression

\frac{1}{6} (2 x + 3) (3 x - 4)

Evaluate

x^{2} + \frac{1}{6} x - 2

Rewrite the expression

\frac{1}{6} \times 6 x^{2} + \frac{1}{6} x - \frac{1}{6} \times 12

Factor out \frac{1}{6} from the expression

\frac{1}{6} (6 x^{2} + x - 12)

Solution

More Steps

Evaluate

6 x^{2} + x - 12

Rewrite the expression

6 x^{2} + (- 8 + 9) x - 12

Calculate

6 x^{2} - 8 x + 9 x - 12

Rewrite the expression

2 x \times 3 x - 2 x \times 4 + 3 \times 3 x - 3 \times 4

Factor out 2 x from the expression

2 x (3 x - 4) + 3 \times 3 x - 3 \times 4

Factor out 3 from the expression

2 x (3 x - 4) + 3 (3 x - 4)

Factor out 3 x - 4 from the expression

(2 x + 3) (3 x - 4)

\frac{1}{6} (2 x + 3) (3 x - 4)

Show Solution

x_{1} = - \frac{3}{2}, x_{2} = \frac{4}{3}

Alternative Form

x_{1} = - 1.5, x_{2} = 1. \dot{3}

Evaluate

x^{2} + \frac{1}{6} x - 2

To find the roots of the expression,set the expression equal to 0

x^{2} + \frac{1}{6} x - 2 = 0

Factor the expression

More Steps

Evaluate

x^{2} + \frac{1}{6} x - 2

Rewrite the expression

\frac{1}{6} \times 6 x^{2} + \frac{1}{6} x - \frac{1}{6} \times 12

Factor out \frac{1}{6} from the expression

\frac{1}{6} (6 x^{2} + x - 12)

Factor the expression

More Steps

Evaluate

6 x^{2} + x - 12

Rewrite the expression

6 x^{2} + (- 8 + 9) x - 12

Calculate

6 x^{2} - 8 x + 9 x - 12

Rewrite the expression

2 x \times 3 x - 2 x \times 4 + 3 \times 3 x - 3 \times 4

Factor out 2 x from the expression

2 x (3 x - 4) + 3 \times 3 x - 3 \times 4

Factor out 3 from the expression

2 x (3 x - 4) + 3 (3 x - 4)

Factor out 3 x - 4 from the expression

(2 x + 3) (3 x - 4)

\frac{1}{6} (2 x + 3) (3 x - 4)

\frac{1}{6} (2 x + 3) (3 x - 4) = 0

Divide the terms

(2 x + 3) (3 x - 4) = 0

When the product of factors equals 0,at least one factor is 0

2 x + 3 = 0 3 x - 4 = 0

Solve the equation for x

More Steps

Evaluate

2 x + 3 = 0

Move the constant to the right-hand side and change its sign

2 x = 0 - 3

Removing 0 doesn't change the value,so remove it from the expression

2 x = - 3

Divide both sides

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

Divide the numbers

x = \frac{- 3}{2}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

x = - \frac{3}{2}

x = - \frac{3}{2} 3 x - 4 = 0

Solve the equation for x

More Steps

Evaluate

3 x - 4 = 0

Move the constant to the right-hand side and change its sign

3 x = 0 + 4

Removing 0 doesn't change the value,so remove it from the expression

3 x = 4

Divide both sides

\frac{3 x}{3} = \frac{4}{3}

Divide the numbers

x = \frac{4}{3}

x = - \frac{3}{2} x = \frac{4}{3}

Solution

x_{1} = - \frac{3}{2}, x_{2} = \frac{4}{3}

Alternative Form

x_{1} = - 1.5, x_{2} = 1. \dot{3}

Show Solution