Solve x^32x^2 - 15x = 0

Question

Solve the equation

x_{1} = - \frac{4 120}{2}, x_{2} = 0, x_{3} = \frac{4 120}{2}

Alternative Form

x_{1} \approx - 1.654875, x_{2} = 0, x_{3} \approx 1.654875

Evaluate

x^{3} \times 2 x^{2} - 15 x = 0

Multiply

More Steps

Evaluate

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

Multiply the terms with the same base by adding their exponents

x^{3 + 2} \times 2

Add the numbers

x^{5} \times 2

Use the commutative property to reorder the terms

2 x^{5}

2 x^{5} - 15 x = 0

Factor the expression

x (2 x^{4} - 15) = 0

Separate the equation into 2 possible cases

x = 0 2 x^{4} - 15 = 0

Solve the equation

More Steps

Evaluate

2 x^{4} - 15 = 0

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

2 x^{4} = 0 + 15

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

2 x^{4} = 15

Divide both sides

\frac{2 x ^{4}}{2} = \frac{15}{2}

Divide the numbers

x^{4} = \frac{15}{2}

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

x = \pm 4 \frac{15}{2}

Simplify the expression

More Steps

Evaluate

4 \frac{15}{2}

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

\frac{4 15}{4 2}

Multiply by the Conjugate

\frac{4 15 \times 4 2 ^{3}}{4 2 \times 4 2 ^{3}}

Simplify

\frac{4 15 \times 4 8}{4 2 \times 4 2 ^{3}}

Multiply the numbers

\frac{4 120}{4 2 \times 4 2 ^{3}}

Multiply the numbers

\frac{4 120}{2}

x = \pm \frac{4 120}{2}

Separate the equation into 2 possible cases

x = \frac{4 120}{2} x = - \frac{4 120}{2}

x = 0 x = \frac{4 120}{2} x = - \frac{4 120}{2}

Solution

x_{1} = - \frac{4 120}{2}, x_{2} = 0, x_{3} = \frac{4 120}{2}

Alternative Form

x_{1} \approx - 1.654875, x_{2} = 0, x_{3} \approx 1.654875

Show Solution