Solve 3x^(2) 2x^(2)=35

Question

Solve the equation

x_{1} = - \frac{4 7560}{6}, x_{2} = \frac{4 7560}{6}

Alternative Form

x_{1} \approx - 1.554101, x_{2} \approx 1.554101

Evaluate

3 x^{2} \times 2 x^{2} = 35

Multiply

More Steps

Evaluate

3 x^{2} \times 2 x^{2}

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

6 x^{2 + 2}

Add the numbers

6 x^{4}

6 x^{4} = 35

Divide both sides

\frac{6 x ^{4}}{6} = \frac{35}{6}

Divide the numbers

x^{4} = \frac{35}{6}

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

x = \pm 4 \frac{35}{6}

Simplify the expression

More Steps

Evaluate

4 \frac{35}{6}

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

\frac{4 35}{4 6}

Multiply by the Conjugate

\frac{4 35 \times 4 6 ^{3}}{4 6 \times 4 6 ^{3}}

Simplify

\frac{4 35 \times 4 216}{4 6 \times 4 6 ^{3}}

Multiply the numbers

More Steps

Evaluate

435 \times 4216

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

4 35 \times 216

Calculate the product

47560

\frac{4 7560}{4 6 \times 4 6 ^{3}}

Multiply the numbers

More Steps

Evaluate

46 \times 4 6^{3}

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

4 6 \times 6^{3}

Calculate the product

4 6^{4}

Reduce the index of the radical and exponent with 4

6

\frac{4 7560}{6}

x = \pm \frac{4 7560}{6}

Separate the equation into 2 possible cases

x = \frac{4 7560}{6} x = - \frac{4 7560}{6}

Solution

x_{1} = - \frac{4 7560}{6}, x_{2} = \frac{4 7560}{6}

Alternative Form

x_{1} \approx - 1.554101, x_{2} \approx 1.554101

Show Solution