Solve x^2 5x-84=0

Question

Solve the equation

x = \frac{3 2100}{5}

Alternative Form

x \approx 2.561158

Evaluate

x^{2} \times 5 x - 84 = 0

Multiply

More Steps

Evaluate

x^{2} \times 5 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 5

Add the numbers

x^{3} \times 5

Use the commutative property to reorder the terms

5 x^{3}

5 x^{3} - 84 = 0

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

5 x^{3} = 0 + 84

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

5 x^{3} = 84

Divide both sides

\frac{5 x ^{3}}{5} = \frac{84}{5}

Divide the numbers

x^{3} = \frac{84}{5}

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

3 x^{3} = 3 \frac{84}{5}

Calculate

x = 3 \frac{84}{5}

Solution

More Steps

Evaluate

3 \frac{84}{5}

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

\frac{3 84}{3 5}

Multiply by the Conjugate

\frac{3 84 \times 3 5 ^{2}}{3 5 \times 3 5 ^{2}}

Simplify

\frac{3 84 \times 3 25}{3 5 \times 3 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

384 \times 325

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

3 84 \times 25

Calculate the product

32100

\frac{3 2100}{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 2100}{5}

x = \frac{3 2100}{5}

Alternative Form

x \approx 2.561158

Show Solution