Solve 20x^3-45x - ScanMath

Question

Factor the expression

5 x (2 x - 3) (2 x + 3)

Evaluate

20 x^{3} - 45 x

Factor out 5 x from the expression

5 x (4 x^{2} - 9)

Solution

More Steps

Evaluate

4 x^{2} - 9

Rewrite the expression in exponential form

(2 x)^{2} - 3^{2}

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

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

5 x (2 x - 3) (2 x + 3)

Show Solution

x_{1} = - \frac{3}{2}, x_{2} = 0, x_{3} = \frac{3}{2}

Alternative Form

x_{1} = - 1.5, x_{2} = 0, x_{3} = 1.5

Evaluate

20 x^{3} - 45 x

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

20 x^{3} - 45 x = 0

Factor the expression

5 x (4 x^{2} - 9) = 0

Divide both sides

x (4 x^{2} - 9) = 0

Separate the equation into 2 possible cases

x = 0 4 x^{2} - 9 = 0

Solve the equation

More Steps

Evaluate

4 x^{2} - 9 = 0

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

4 x^{2} = 0 + 9

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

4 x^{2} = 9

Divide both sides

\frac{4 x ^{2}}{4} = \frac{9}{4}

Divide the numbers

x^{2} = \frac{9}{4}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm \frac{9}{4}

Simplify the expression

More Steps

Evaluate

\frac{9}{4}

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

\frac{9}{4}

Simplify the radical expression

\frac{3}{4}

Simplify the radical expression

\frac{3}{2}

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

Separate the equation into 2 possible cases

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

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

Solution

x_{1} = - \frac{3}{2}, x_{2} = 0, x_{3} = \frac{3}{2}

Alternative Form

x_{1} = - 1.5, x_{2} = 0, x_{3} = 1.5

Show Solution