Solve 52x=3*2x^2*5x^2*3x

Question

Solve the equation

x_{1} = - \frac{4 26 \times 4 5 ^{3}}{45}, x_{2} = 0, x_{3} = \frac{4 26 \times 4 5 ^{3}}{45}

Alternative Form

x_{1} \approx - 0.871847, x_{2} = 0, x_{3} \approx 0.871847

Evaluate

52 x = 3 \times 2 x^{2} \times 5 x^{2} \times 3 x

Multiply

More Steps

Evaluate

3 \times 2 x^{2} \times 5 x^{2} \times 3 x

Multiply the terms

More Steps

Evaluate

3 \times 2 \times 5 \times 3

Multiply the terms

6 \times 5 \times 3

Multiply the terms

30 \times 3

Multiply the numbers

90

90 x^{2} \times x^{2} \times x

Multiply the terms with the same base by adding their exponents

90 x^{2 + 2 + 1}

Add the numbers

90 x^{5}

52 x = 90 x^{5}

Add or subtract both sides

52 x - 90 x^{5} = 0

Factor the expression

2 x (26 - 45 x^{4}) = 0

Divide both sides

x (26 - 45 x^{4}) = 0

Separate the equation into 2 possible cases

x = 0 26 - 45 x^{4} = 0

Solve the equation

More Steps

Evaluate

26 - 45 x^{4} = 0

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

- 45 x^{4} = 0 - 26

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

- 45 x^{4} = - 26

Change the signs on both sides of the equation

45 x^{4} = 26

Divide both sides

\frac{45 x ^{4}}{45} = \frac{26}{45}

Divide the numbers

x^{4} = \frac{26}{45}

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

x = \pm 4 \frac{26}{45}

Simplify the expression

More Steps

Evaluate

4 \frac{26}{45}

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

\frac{4 26}{4 45}

Multiply by the Conjugate

\frac{4 26 \times 4 4 5 ^{3}}{4 45 \times 4 4 5 ^{3}}

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

\frac{4 26 \times 4 5 ^{3}}{4 45 \times 4 4 5 ^{3}}

Multiply the numbers

\frac{4 26 \times 4 5 ^{3}}{45}

x = \pm \frac{4 26 \times 4 5 ^{3}}{45}

Separate the equation into 2 possible cases

x = \frac{4 26 \times 4 5 ^{3}}{45} x = - \frac{4 26 \times 4 5 ^{3}}{45}

x = 0 x = \frac{4 26 \times 4 5 ^{3}}{45} x = - \frac{4 26 \times 4 5 ^{3}}{45}

Solution

x_{1} = - \frac{4 26 \times 4 5 ^{3}}{45}, x_{2} = 0, x_{3} = \frac{4 26 \times 4 5 ^{3}}{45}

Alternative Form

x_{1} \approx - 0.871847, x_{2} = 0, x_{3} \approx 0.871847

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