Solve 9x^47x^2 - 2 = 0

Question

Solve the equation

x_{1} = - \frac{6 2 \times 6 3 ^{5}}{63}, x_{2} = \frac{6 2 \times 6 3 ^{5}}{63}

Alternative Form

x_{1} \approx - 0.562706, x_{2} \approx 0.562706

Evaluate

9 x^{4} \times 7 x^{2} - 2 = 0

Multiply

More Steps

Evaluate

9 x^{4} \times 7 x^{2}

Multiply the terms

63 x^{4} \times x^{2}

Multiply the terms with the same base by adding their exponents

63 x^{4 + 2}

Add the numbers

63 x^{6}

63 x^{6} - 2 = 0

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

63 x^{6} = 0 + 2

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

63 x^{6} = 2

Divide both sides

\frac{63 x ^{6}}{63} = \frac{2}{63}

Divide the numbers

x^{6} = \frac{2}{63}

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

x = \pm 6 \frac{2}{63}

Simplify the expression

More Steps

Evaluate

6 \frac{2}{63}

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

\frac{6 2}{6 63}

Multiply by the Conjugate

\frac{6 2 \times 6 6 3 ^{5}}{6 63 \times 6 6 3 ^{5}}

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

\frac{6 2 \times 6 3 ^{5}}{6 63 \times 6 6 3 ^{5}}

Multiply the numbers

More Steps

Evaluate

663 \times 6 6 3^{5}

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

6 63 \times 6 3^{5}

Calculate the product

6 6 3^{6}

Reduce the index of the radical and exponent with 6

63

\frac{6 2 \times 6 3 ^{5}}{63}

x = \pm \frac{6 2 \times 6 3 ^{5}}{63}

Separate the equation into 2 possible cases

x = \frac{6 2 \times 6 3 ^{5}}{63} x = - \frac{6 2 \times 6 3 ^{5}}{63}

Solution

x_{1} = - \frac{6 2 \times 6 3 ^{5}}{63}, x_{2} = \frac{6 2 \times 6 3 ^{5}}{63}

Alternative Form

x_{1} \approx - 0.562706, x_{2} \approx 0.562706

Show Solution