Solve 2x^2 5x-14=0

Question

Solve the equation

x = \frac{3 175}{5}

Alternative Form

x \approx 1.118689

Evaluate

2 x^{2} \times 5 x - 14 = 0

Multiply

More Steps

Evaluate

2 x^{2} \times 5 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} - 14 = 0

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

10 x^{3} = 0 + 14

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

10 x^{3} = 14

Divide both sides

\frac{10 x ^{3}}{10} = \frac{14}{10}

Divide the numbers

x^{3} = \frac{14}{10}

Cancel out the common factor 2

x^{3} = \frac{7}{5}

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

3 x^{3} = 3 \frac{7}{5}

Calculate

x = 3 \frac{7}{5}

Solution

More Steps

Evaluate

3 \frac{7}{5}

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

\frac{3 7}{3 5}

Multiply by the Conjugate

\frac{3 7 \times 3 5 ^{2}}{3 5 \times 3 5 ^{2}}

Simplify

\frac{3 7 \times 3 25}{3 5 \times 3 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

37 \times 325

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

3 7 \times 25

Calculate the product

3175

\frac{3 175}{3 5 \times 3 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

35 \times 3 5^{2}

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

3 5 \times 5^{2}

Calculate the product

3 5^{3}

Reduce the index of the radical and exponent with 3

5

\frac{3 175}{5}

x = \frac{3 175}{5}

Alternative Form

x \approx 1.118689

Show Solution