Solve 2(x^3) =x 7

Question

Solve the equation

x_{1} = - \frac{14}{2}, x_{2} = 0, x_{3} = \frac{14}{2}

Alternative Form

x_{1} \approx - 1.870829, x_{2} = 0, x_{3} \approx 1.870829

Evaluate

2 x^{3} = x \times 7

Use the commutative property to reorder the terms

2 x^{3} = 7 x

Add or subtract both sides

2 x^{3} - 7 x = 0

Factor the expression

x (2 x^{2} - 7) = 0

Separate the equation into 2 possible cases

x = 0 2 x^{2} - 7 = 0

Solve the equation

More Steps

Evaluate

2 x^{2} - 7 = 0

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

2 x^{2} = 0 + 7

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

2 x^{2} = 7

Divide both sides

\frac{2 x ^{2}}{2} = \frac{7}{2}

Divide the numbers

x^{2} = \frac{7}{2}

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

x = \pm \frac{7}{2}

Simplify the expression

More Steps

Evaluate

\frac{7}{2}

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

\frac{7}{2}

Multiply by the Conjugate

\frac{7 \times 2}{2 \times 2}

Multiply the numbers

\frac{14}{2 \times 2}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{14}{2}

x = \pm \frac{14}{2}

Separate the equation into 2 possible cases

x = \frac{14}{2} x = - \frac{14}{2}

x = 0 x = \frac{14}{2} x = - \frac{14}{2}

Solution

x_{1} = - \frac{14}{2}, x_{2} = 0, x_{3} = \frac{14}{2}

Alternative Form

x_{1} \approx - 1.870829, x_{2} = 0, x_{3} \approx 1.870829

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