Solve 10x^2 20x-65=0

Question

Solve the equation

x = \frac{3 325}{10}

Alternative Form

x \approx 0.687534

Evaluate

10 x^{2} \times 20 x - 65 = 0

Multiply

More Steps

Evaluate

10 x^{2} \times 20 x

Multiply the terms

200 x^{2} \times x

Multiply the terms with the same base by adding their exponents

200 x^{2 + 1}

Add the numbers

200 x^{3}

200 x^{3} - 65 = 0

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

200 x^{3} = 0 + 65

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

200 x^{3} = 65

Divide both sides

\frac{200 x ^{3}}{200} = \frac{65}{200}

Divide the numbers

x^{3} = \frac{65}{200}

Cancel out the common factor 5

x^{3} = \frac{13}{40}

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

3 x^{3} = 3 \frac{13}{40}

Calculate

x = 3 \frac{13}{40}

Solution

More Steps

Evaluate

3 \frac{13}{40}

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

\frac{3 13}{3 40}

Simplify the radical expression

More Steps

Evaluate

340

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

3 8 \times 5

Write the number in exponential form with the base of 2

3 2^{3} \times 5

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

3 2^{3} \times 35

Reduce the index of the radical and exponent with 3

235

\frac{3 13}{2 3 5}

Multiply by the Conjugate

\frac{3 13 \times 3 5 ^{2}}{2 3 5 \times 3 5 ^{2}}

Simplify

\frac{3 13 \times 3 25}{2 3 5 \times 3 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

313 \times 325

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

3 13 \times 25

Calculate the product

3325

\frac{3 325}{2 3 5 \times 3 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

235 \times 3 5^{2}

Multiply the terms

2 \times 5

Multiply the terms

10

\frac{3 325}{10}

x = \frac{3 325}{10}

Alternative Form

x \approx 0.687534

Show Solution