Solve z^(2) 2z-3=0 - Socratic AI (ScanMath)

Question

Solve the equation

z = \frac{3 12}{2}

Alternative Form

z \approx 1.144714

Evaluate

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

Multiply

More Steps

Evaluate

z^{2} \times 2 z

Multiply the terms with the same base by adding their exponents

z^{2 + 1} \times 2

Add the numbers

z^{3} \times 2

Use the commutative property to reorder the terms

2 z^{3}

2 z^{3} - 3 = 0

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

2 z^{3} = 0 + 3

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

2 z^{3} = 3

Divide both sides

\frac{2 z ^{3}}{2} = \frac{3}{2}

Divide the numbers

z^{3} = \frac{3}{2}

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

3 z^{3} = 3 \frac{3}{2}

Calculate

z = 3 \frac{3}{2}

Solution

More Steps

Evaluate

3 \frac{3}{2}

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

\frac{3 3}{3 2}

Multiply by the Conjugate

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

Simplify

\frac{3 3 \times 3 4}{3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

33 \times 34

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

3 3 \times 4

Calculate the product

312

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

Multiply the numbers

More Steps

Evaluate

32 \times 3 2^{2}

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

3 2 \times 2^{2}

Calculate the product

3 2^{3}

Reduce the index of the radical and exponent with 3

2

\frac{3 12}{2}

z = \frac{3 12}{2}

Alternative Form

z \approx 1.144714

Show Solution