Solve 648w-1029w^4

Question

Factor the expression

3 w (6 - 7 w) (36 + 42 w + 49 w^{2})

Evaluate

648 w - 1029 w^{4}

Factor out 3 w from the expression

3 w (216 - 343 w^{3})

Solution

More Steps

Evaluate

216 - 343 w^{3}

Rewrite the expression in exponential form

6^{3} - (7 w)^{3}

Use a^{3} - b^{3} = (a - b) (a^{2} + ab + b^{2}) to factor the expression

(6 - 7 w) (6^{2} + 6 \times 7 w + (7 w)^{2})

Evaluate

(6 - 7 w) (36 + 6 \times 7 w + (7 w)^{2})

Evaluate

(6 - 7 w) (36 + 42 w + (7 w)^{2})

Evaluate

More Steps

Evaluate

(7 w)^{2}

To raise a product to a power,raise each factor to that power

7^{2} w^{2}

Evaluate the power

49 w^{2}

(6 - 7 w) (36 + 42 w + 49 w^{2})

3 w (6 - 7 w) (36 + 42 w + 49 w^{2})

Show Solution

w_{1} = 0, w_{2} = \frac{6}{7}

Alternative Form

w_{1} = 0, w_{2} = 0. \dot{8} 5714 \dot{2}

Evaluate

648 w - 1029 w^{4}

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

648 w - 1029 w^{4} = 0

Factor the expression

3 w (216 - 343 w^{3}) = 0

Divide both sides

w (216 - 343 w^{3}) = 0

Separate the equation into 2 possible cases

w = 0 216 - 343 w^{3} = 0

Solve the equation

More Steps

Evaluate

216 - 343 w^{3} = 0

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

- 343 w^{3} = 0 - 216

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

- 343 w^{3} = - 216

Change the signs on both sides of the equation

343 w^{3} = 216

Divide both sides

\frac{343 w ^{3}}{343} = \frac{216}{343}

Divide the numbers

w^{3} = \frac{216}{343}

Take the 3 -th root on both sides of the equation

3 w^{3} = 3 \frac{216}{343}

Calculate

w = 3 \frac{216}{343}

Simplify the root

More Steps

Evaluate

3 \frac{216}{343}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{3 216}{3 343}

Simplify the radical expression

\frac{6}{3 343}

Simplify the radical expression

\frac{6}{7}

w = \frac{6}{7}

w = 0 w = \frac{6}{7}

Solution

w_{1} = 0, w_{2} = \frac{6}{7}

Alternative Form

w_{1} = 0, w_{2} = 0. \dot{8} 5714 \dot{2}

Show Solution