Solve 10x^(2) 152x-10=0

Question

Solve the equation

x = \frac{3 361}{38}

Alternative Form

x \approx 0.187378

Evaluate

10 x^{2} \times 152 x - 10 = 0

Multiply

More Steps

Evaluate

10 x^{2} \times 152 x

Multiply the terms

1520 x^{2} \times x

Multiply the terms with the same base by adding their exponents

1520 x^{2 + 1}

Add the numbers

1520 x^{3}

1520 x^{3} - 10 = 0

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

1520 x^{3} = 0 + 10

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

1520 x^{3} = 10

Divide both sides

\frac{1520 x ^{3}}{1520} = \frac{10}{1520}

Divide the numbers

x^{3} = \frac{10}{1520}

Cancel out the common factor 10

x^{3} = \frac{1}{152}

Take the 3 -th root on both sides of the equation

3 x^{3} = 3 \frac{1}{152}

Calculate

x = 3 \frac{1}{152}

Solution

More Steps

Evaluate

3 \frac{1}{152}

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

\frac{3 1}{3 152}

Simplify the radical expression

\frac{1}{3 152}

Simplify the radical expression

More Steps

Evaluate

3152

Write the expression as a product where the root of one of the factors can be evaluated

3 8 \times 19

Write the number in exponential form with the base of 2

3 2^{3} \times 19

The root of a product is equal to the product of the roots of each factor

3 2^{3} \times 319

Reduce the index of the radical and exponent with 3

2319

\frac{1}{2 3 19}

Multiply by the Conjugate

\frac{3 1 9 ^{2}}{2 3 19 \times 3 1 9 ^{2}}

Simplify

\frac{3 361}{2 3 19 \times 3 1 9 ^{2}}

Multiply the numbers

More Steps

Evaluate

2319 \times 3 1 9^{2}

Multiply the terms

2 \times 19

Multiply the terms

38

\frac{3 361}{38}

x = \frac{3 361}{38}

Alternative Form

x \approx 0.187378

Show Solution