Solve z^2 10z-24=0

Question

Solve the equation

z = \frac{3 300}{5}

Alternative Form

z \approx 1.338866

Evaluate

z^{2} \times 10 z - 24 = 0

Multiply

More Steps

Evaluate

z^{2} \times 10 z

Multiply the terms with the same base by adding their exponents

z^{2 + 1} \times 10

Add the numbers

z^{3} \times 10

Use the commutative property to reorder the terms

10 z^{3}

10 z^{3} - 24 = 0

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

10 z^{3} = 0 + 24

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

10 z^{3} = 24

Divide both sides

\frac{10 z ^{3}}{10} = \frac{24}{10}

Divide the numbers

z^{3} = \frac{24}{10}

Cancel out the common factor 2

z^{3} = \frac{12}{5}

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

3 z^{3} = 3 \frac{12}{5}

Calculate

z = 3 \frac{12}{5}

Solution

More Steps

Evaluate

3 \frac{12}{5}

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

\frac{3 12}{3 5}

Multiply by the Conjugate

\frac{3 12 \times 3 5 ^{2}}{3 5 \times 3 5 ^{2}}

Simplify

\frac{3 12 \times 3 25}{3 5 \times 3 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

312 \times 325

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

3 12 \times 25

Calculate the product

3300

\frac{3 300}{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{3 300}{5}

z = \frac{3 300}{5}

Alternative Form

z \approx 1.338866

Show Solution