Solve 3/4 * x ^ 2 / 9 - 1/6 * x - 4

Question

Simplify the expression

\frac{x ^{2} - 2 x - 48}{12}

Evaluate

\frac{3}{4} \times \frac{x ^{2}}{9} - \frac{1}{6} x - 4

Multiply the terms

More Steps

Evaluate

\frac{3}{4} \times \frac{x ^{2}}{9}

Cancel out the common factor 3

\frac{1}{4} \times \frac{x ^{2}}{3}

Multiply the terms

\frac{x ^{2}}{4 \times 3}

Multiply the terms

\frac{x ^{2}}{12}

\frac{x ^{2}}{12} - \frac{1}{6} x - 4

Rewrite the expression

\frac{x ^{2}}{12} - \frac{x}{6} - 4

Reduce fractions to a common denominator

\frac{x ^{2}}{12} - \frac{x \times 2}{6 \times 2} - \frac{4 \times 6 \times 2}{6 \times 2}

Multiply the numbers

\frac{x ^{2}}{12} - \frac{x \times 2}{12} - \frac{4 \times 6 \times 2}{6 \times 2}

Multiply the numbers

\frac{x ^{2}}{12} - \frac{x \times 2}{12} - \frac{4 \times 6 \times 2}{12}

Write all numerators above the common denominator

\frac{x ^{2} - x \times 2 - 4 \times 6 \times 2}{12}

Use the commutative property to reorder the terms

\frac{x ^{2} - 2 x - 4 \times 6 \times 2}{12}

Solution

More Steps

Evaluate

4 \times 6 \times 2

Multiply the terms

24 \times 2

Multiply the numbers

48

\frac{x ^{2} - 2 x - 48}{12}

Show Solution

Find the roots

x_{1} = - 6, x_{2} = 8

Evaluate

\frac{3}{4} \times \frac{x ^{2}}{9} - \frac{1}{6} x - 4

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

\frac{3}{4} \times \frac{x ^{2}}{9} - \frac{1}{6} x - 4 = 0

Multiply the terms

More Steps

Evaluate

\frac{3}{4} \times \frac{x ^{2}}{9}

Cancel out the common factor 3

\frac{1}{4} \times \frac{x ^{2}}{3}

Multiply the terms

\frac{x ^{2}}{4 \times 3}

Multiply the terms

\frac{x ^{2}}{12}

\frac{x ^{2}}{12} - \frac{1}{6} x - 4 = 0

Subtract the terms

More Steps

Simplify

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

Rewrite the expression

\frac{x ^{2}}{12} - \frac{x}{6}

Reduce fractions to a common denominator

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

Multiply the numbers

\frac{x ^{2}}{12} - \frac{x \times 2}{12}

Write all numerators above the common denominator

\frac{x ^{2} - x \times 2}{12}

Use the commutative property to reorder the terms

\frac{x ^{2} - 2 x}{12}

\frac{x ^{2} - 2 x}{12} - 4 = 0

Subtract the terms

More Steps

Simplify

\frac{x ^{2} - 2 x}{12} - 4

Reduce fractions to a common denominator

\frac{x ^{2} - 2 x}{12} - \frac{4 \times 12}{12}

Write all numerators above the common denominator

\frac{x ^{2} - 2 x - 4 \times 12}{12}

Multiply the numbers

\frac{x ^{2} - 2 x - 48}{12}

\frac{x ^{2} - 2 x - 48}{12} = 0

Simplify

x^{2} - 2 x - 48 = 0

Factor the expression

More Steps

Evaluate

x^{2} - 2 x - 48

Rewrite the expression

x^{2} + (6 - 8) x - 48

Calculate

x^{2} + 6 x - 8 x - 48

Rewrite the expression

x \times x + x \times 6 - 8 x - 8 \times 6

Factor out x from the expression

x (x + 6) - 8 x - 8 \times 6

Factor out - 8 from the expression

x (x + 6) - 8 (x + 6)

Factor out x + 6 from the expression

(x - 8) (x + 6)

(x - 8) (x + 6) = 0

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

x - 8 = 0 x + 6 = 0

Solve the equation for x

More Steps

Evaluate

x - 8 = 0

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

x = 0 + 8

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

x = 8

x = 8 x + 6 = 0

Solve the equation for x

More Steps

Evaluate

x + 6 = 0

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

x = 0 - 6

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

x = - 6

x = 8 x = - 6

Solution

x_{1} = - 6, x_{2} = 8

Show Solution