Solve 5x^2 2x - 7 = 0

Question

5 x^{2} \times 2 x - 7 = 0

Solve the equation

x = \frac{3 700}{10}

Alternative Form

x \approx 0.887904

Evaluate

5 x^{2} \times 2 x - 7 = 0

Multiply

More Steps

Evaluate

5 x^{2} \times 2 x

Multiply the terms

10 x^{2} \times x

Multiply the terms with the same base by adding their exponents

10 x^{2 + 1}

Add the numbers

10 x^{3}

10 x^{3} - 7 = 0

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

10 x^{3} = 0 + 7

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

10 x^{3} = 7

Divide both sides

\frac{10 x ^{3}}{10} = \frac{7}{10}

Divide the numbers

x^{3} = \frac{7}{10}

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

3 x^{3} = 3 \frac{7}{10}

Calculate

x = 3 \frac{7}{10}

Solution

More Steps

Evaluate

3 \frac{7}{10}

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

\frac{3 7}{3 10}

Multiply by the Conjugate

\frac{3 7 \times 3 1 0 ^{2}}{3 10 \times 3 1 0 ^{2}}

Simplify

\frac{3 7 \times 3 100}{3 10 \times 3 1 0 ^{2}}

Multiply the numbers

More Steps

Evaluate

37 \times 3100

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

3 7 \times 100

Calculate the product

3700

\frac{3 700}{3 10 \times 3 1 0 ^{2}}

Multiply the numbers

More Steps

Evaluate

310 \times 3 1 0^{2}

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

3 10 \times 1 0^{2}

Calculate the product

3 1 0^{3}

Reduce the index of the radical and exponent with 3

10

\frac{3 700}{10}

x = \frac{3 700}{10}

Alternative Form

x \approx 0.887904

Show Solution