Solve x*x^2 6x 9 = 12

Question

Solve the equation

x_{1} = - \frac{4 18}{3}, x_{2} = \frac{4 18}{3}

Alternative Form

x_{1} \approx - 0.686589, x_{2} \approx 0.686589

Evaluate

x \times x^{2} \times 6 x \times 9 = 12

Multiply

More Steps

Evaluate

x \times x^{2} \times 6 x \times 9

Multiply the terms with the same base by adding their exponents

x^{1 + 2 + 1} \times 6 \times 9

Add the numbers

x^{4} \times 6 \times 9

Multiply the terms

x^{4} \times 54

Use the commutative property to reorder the terms

54 x^{4}

54 x^{4} = 12

Divide both sides

\frac{54 x ^{4}}{54} = \frac{12}{54}

Divide the numbers

x^{4} = \frac{12}{54}

Cancel out the common factor 6

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

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

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

Simplify the expression

More Steps

Evaluate

4 \frac{2}{9}

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

\frac{4 2}{4 9}

Simplify the radical expression

More Steps

Evaluate

49

Write the number in exponential form with the base of 3

4 3^{2}

Reduce the index of the radical and exponent with 2

3

\frac{4 2}{3}

Multiply by the Conjugate

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

Multiply the numbers

More Steps

Evaluate

42 \times 3

Use n a = mn a^{m} to expand the expression

42 \times 4 3^{2}

The product of roots with the same index is equal to the root of the product

4 2 \times 3^{2}

Calculate the product

418

\frac{4 18}{3 \times 3}

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

\frac{4 18}{3}

x = \pm \frac{4 18}{3}

Separate the equation into 2 possible cases

x = \frac{4 18}{3} x = - \frac{4 18}{3}

Solution

x_{1} = - \frac{4 18}{3}, x_{2} = \frac{4 18}{3}

Alternative Form

x_{1} \approx - 0.686589, x_{2} \approx 0.686589

Show Solution