Solve 9x^(2/3) -62x^(1/3) - 7

Question

Simplify the expression

Solution

9 3 x^{2} - 62 3 x - 7

Evaluate

9 x^{\frac{2}{3}} - 62 x^{\frac{1}{3}} - 7

Solution

9 3 x^{2} - 62 3 x - 7

Show Solution

Factor the expression

Factor

(3 x - 7) (9 3 x + 1)

Evaluate

9 x^{\frac{2}{3}} - 62 x^{\frac{1}{3}} - 7

Rewrite the expression

9 x^{\frac{2}{3}} + (1 - 63) x^{\frac{1}{3}} - 7

Calculate

9 x^{\frac{2}{3}} + x^{\frac{1}{3}} - 63 x^{\frac{1}{3}} - 7

Rewrite the expression

x^{\frac{1}{3}} \times 9 x^{\frac{1}{3}} + x^{\frac{1}{3}} - 7 \times 9 x^{\frac{1}{3}} - 7

Factor out x^{\frac{1}{3}} from the expression

x^{\frac{1}{3}} (9 x^{\frac{1}{3}} + 1) - 7 \times 9 x^{\frac{1}{3}} - 7

Factor out - 7 from the expression

x^{\frac{1}{3}} (9 x^{\frac{1}{3}} + 1) - 7 (9 x^{\frac{1}{3}} + 1)

Factor out 9 x^{\frac{1}{3}} + 1 from the expression

(x^{\frac{1}{3}} - 7) (9 x^{\frac{1}{3}} + 1)

Solution

(3 x - 7) (9 3 x + 1)

Show Solution

Find the roots

Find the roots of the algebra expression

x_{1} = - \frac{1}{729}, x_{2} = 343

Alternative Form

x_{1} \approx - 0.001372, x_{2} = 343

Evaluate

9 x^{\frac{2}{3}} - 62 x^{\frac{1}{3}} - 7

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

9 x^{\frac{2}{3}} - 62 x^{\frac{1}{3}} - 7 = 0

Solve the equation using substitution t = x^{\frac{1}{3}}

9 t^{2} - 62 t - 7 = 0

Factor the expression

More Steps

Evaluate

9 t^{2} - 62 t - 7

Rewrite the expression

9 t^{2} + (1 - 63) t - 7

Calculate

9 t^{2} + t - 63 t - 7

Rewrite the expression

t \times 9 t + t - 7 \times 9 t - 7

Factor out t from the expression

t (9 t + 1) - 7 \times 9 t - 7

Factor out - 7 from the expression

t (9 t + 1) - 7 (9 t + 1)

Factor out 9 t + 1 from the expression

(t - 7) (9 t + 1)

(t - 7) (9 t + 1) = 0

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

t - 7 = 0 9 t + 1 = 0

Solve the equation for t

More Steps

Evaluate

t - 7 = 0

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

t = 0 + 7

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

t = 7

t = 7 9 t + 1 = 0

Solve the equation for t

More Steps

Evaluate

9 t + 1 = 0

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

9 t = 0 - 1

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

9 t = - 1

Divide both sides

\frac{9 t}{9} = \frac{- 1}{9}

Divide the numbers

t = \frac{- 1}{9}

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

t = - \frac{1}{9}

t = 7 t = - \frac{1}{9}

Substitute back

x^{\frac{1}{3}} = 7 x^{\frac{1}{3}} = - \frac{1}{9}

Solve the equation for x

More Steps

Substitute back

x^{\frac{1}{3}} = 7

Raise both sides of the equation to the 3 -th power to eliminate the isolated 3 -th root

(x^{\frac{1}{3}})^{3} = 7^{3}

Calculate

x = 343

x = 343 x^{\frac{1}{3}} = - \frac{1}{9}

Solve the equation for x

More Steps

Substitute back

x^{\frac{1}{3}} = - \frac{1}{9}

Raise both sides of the equation to the 3 -th power to eliminate the isolated 3 -th root

(x^{\frac{1}{3}})^{3} = (- \frac{1}{9})^{3}

Calculate

x = - \frac{1}{729}

x = 343 x = - \frac{1}{729}

Solution

x_{1} = - \frac{1}{729}, x_{2} = 343

Alternative Form

x_{1} \approx - 0.001372, x_{2} = 343

Show Solution

9x^(2/3) 62x^(1/3) 7

Simplify the expression

Solution

Factor the expression

Factor

Find the roots

Find the roots of the algebra expression