Solve 52x=51x^3 - ScanMath

Question

Solve the equation

x_{1} = - \frac{2 663}{51}, x_{2} = 0, x_{3} = \frac{2 663}{51}

Alternative Form

x_{1} \approx - 1.009756, x_{2} = 0, x_{3} \approx 1.009756

Evaluate

52 x = 51 x^{3}

Add or subtract both sides

52 x - 51 x^{3} = 0

Factor the expression

x (52 - 51 x^{2}) = 0

Separate the equation into 2 possible cases

x = 0 52 - 51 x^{2} = 0

Solve the equation

More Steps

Evaluate

52 - 51 x^{2} = 0

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

- 51 x^{2} = 0 - 52

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

- 51 x^{2} = - 52

Change the signs on both sides of the equation

51 x^{2} = 52

Divide both sides

\frac{51 x ^{2}}{51} = \frac{52}{51}

Divide the numbers

x^{2} = \frac{52}{51}

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

x = \pm \frac{52}{51}

Simplify the expression

More Steps

Evaluate

\frac{52}{51}

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

\frac{52}{51}

Simplify the radical expression

\frac{2 13}{51}

Multiply by the Conjugate

\frac{2 13 \times 51}{51 \times 51}

Multiply the numbers

\frac{2 663}{51 \times 51}

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

\frac{2 663}{51}

x = \pm \frac{2 663}{51}

Separate the equation into 2 possible cases

x = \frac{2 663}{51} x = - \frac{2 663}{51}

x = 0 x = \frac{2 663}{51} x = - \frac{2 663}{51}

Solution

x_{1} = - \frac{2 663}{51}, x_{2} = 0, x_{3} = \frac{2 663}{51}

Alternative Form

x_{1} \approx - 1.009756, x_{2} = 0, x_{3} \approx 1.009756

Show Solution