Solve z^2 3z-28 - ScanMath

Question

Simplify the expression

3 z^{3} - 28

Evaluate

z^{2} \times 3 z - 28

Solution

More Steps

Evaluate

z^{2} \times 3 z

Multiply the terms with the same base by adding their exponents

z^{2 + 1} \times 3

Add the numbers

z^{3} \times 3

Use the commutative property to reorder the terms

3 z^{3}

3 z^{3} - 28

Show Solution

z = \frac{3 252}{3}

Alternative Form

z \approx 2.105453

Evaluate

z^{2} \times 3 z - 28

To find the roots of the expression,set the expression equal to 0

z^{2} \times 3 z - 28 = 0

Multiply

More Steps

Multiply the terms

z^{2} \times 3 z

Multiply the terms with the same base by adding their exponents

z^{2 + 1} \times 3

Add the numbers

z^{3} \times 3

Use the commutative property to reorder the terms

3 z^{3}

3 z^{3} - 28 = 0

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

3 z^{3} = 0 + 28

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

3 z^{3} = 28

Divide both sides

\frac{3 z ^{3}}{3} = \frac{28}{3}

Divide the numbers

z^{3} = \frac{28}{3}

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

3 z^{3} = 3 \frac{28}{3}

Calculate

z = 3 \frac{28}{3}

Solution

More Steps

Evaluate

3 \frac{28}{3}

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

\frac{3 28}{3 3}

Multiply by the Conjugate

\frac{3 28 \times 3 3 ^{2}}{3 3 \times 3 3 ^{2}}

Simplify

\frac{3 28 \times 3 9}{3 3 \times 3 3 ^{2}}

Multiply the numbers

More Steps

Evaluate

328 \times 39

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

3 28 \times 9

Calculate the product

3252

\frac{3 252}{3 3 \times 3 3 ^{2}}

Multiply the numbers

More Steps

Evaluate

33 \times 3 3^{2}

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

3 3 \times 3^{2}

Calculate the product

3 3^{3}

Reduce the index of the radical and exponent with 3

3

\frac{3 252}{3}

z = \frac{3 252}{3}

Alternative Form

z \approx 2.105453

Show Solution