Solve 5x-42x^3 - ScanMath

Question

Factor the expression

x (5 - 42 x^{2})

Evaluate

5 x - 42 x^{3}

Rewrite the expression

x \times 5 - x \times 42 x^{2}

Solution

x (5 - 42 x^{2})

Show Solution

x_{1} = - \frac{210}{42}, x_{2} = 0, x_{3} = \frac{210}{42}

Alternative Form

x_{1} \approx - 0.345033, x_{2} = 0, x_{3} \approx 0.345033

Evaluate

5 x - 42 x^{3}

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

5 x - 42 x^{3} = 0

Factor the expression

x (5 - 42 x^{2}) = 0

Separate the equation into 2 possible cases

x = 0 5 - 42 x^{2} = 0

Solve the equation

More Steps

Evaluate

5 - 42 x^{2} = 0

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

- 42 x^{2} = 0 - 5

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

- 42 x^{2} = - 5

Change the signs on both sides of the equation

42 x^{2} = 5

Divide both sides

\frac{42 x ^{2}}{42} = \frac{5}{42}

Divide the numbers

x^{2} = \frac{5}{42}

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

x = \pm \frac{5}{42}

Simplify the expression

More Steps

Evaluate

\frac{5}{42}

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

\frac{5}{42}

Multiply by the Conjugate

\frac{5 \times 42}{42 \times 42}

Multiply the numbers

\frac{210}{42 \times 42}

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

\frac{210}{42}

x = \pm \frac{210}{42}

Separate the equation into 2 possible cases

x = \frac{210}{42} x = - \frac{210}{42}

x = 0 x = \frac{210}{42} x = - \frac{210}{42}

Solution

x_{1} = - \frac{210}{42}, x_{2} = 0, x_{3} = \frac{210}{42}

Alternative Form

x_{1} \approx - 0.345033, x_{2} = 0, x_{3} \approx 0.345033

Show Solution