Solve 1x^(2) 5/2 x- 3/2 =0

Question

Solve the equation

x = \frac{3 75}{5}

Alternative Form

x \approx 0.843433

Evaluate

1 \times x^{2} \times \frac{5}{2} x - \frac{3}{2} = 0

Multiply the terms

More Steps

Evaluate

1 \times x^{2} \times \frac{5}{2} x

Rewrite the expression

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

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times \frac{5}{2}

Add the numbers

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

Use the commutative property to reorder the terms

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

\frac{5}{2} x^{3} - \frac{3}{2} = 0

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

\frac{5}{2} x^{3} = 0 + \frac{3}{2}

Add the terms

\frac{5}{2} x^{3} = \frac{3}{2}

Multiply by the reciprocal

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

Multiply

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

Multiply

More Steps

Evaluate

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

Reduce the numbers

3 \times \frac{1}{5}

Multiply the numbers

\frac{3}{5}

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

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

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

Calculate

x = 3 \frac{3}{5}

Solution

More Steps

Evaluate

3 \frac{3}{5}

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

\frac{3 3}{3 5}

Multiply by the Conjugate

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

Simplify

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

Multiply the numbers

More Steps

Evaluate

33 \times 325

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

3 3 \times 25

Calculate the product

375

\frac{3 75}{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 75}{5}

x = \frac{3 75}{5}

Alternative Form

x \approx 0.843433

Show Solution