Solve s^2012+512 - ScanMath

Question

Simplify the expression

12 s^{2} + 512

Evaluate

s^{2} \times 12 + 512

Solution

12 s^{2} + 512

Show Solution

4 (3 s^{2} + 128)

Evaluate

s^{2} \times 12 + 512

Use the commutative property to reorder the terms

12 s^{2} + 512

Solution

4 (3 s^{2} + 128)

Show Solution

s_{1} = - \frac{8 6}{3} i, s_{2} = \frac{8 6}{3} i

Alternative Form

s_{1} \approx - 6.531973 i, s_{2} \approx 6.531973 i

Evaluate

s^{2} \times 12 + 512

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

s^{2} \times 12 + 512 = 0

Use the commutative property to reorder the terms

12 s^{2} + 512 = 0

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

12 s^{2} = 0 - 512

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

12 s^{2} = - 512

Divide both sides

\frac{12 s ^{2}}{12} = \frac{- 512}{12}

Divide the numbers

s^{2} = \frac{- 512}{12}

Divide the numbers

More Steps

Evaluate

\frac{- 512}{12}

Cancel out the common factor 4

\frac{- 128}{3}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

- \frac{128}{3}

s^{2} = - \frac{128}{3}

Take the root of both sides of the equation and remember to use both positive and negative roots

s = \pm - \frac{128}{3}

Simplify the expression

More Steps

Evaluate

- \frac{128}{3}

Evaluate the power

\frac{128}{3} \times - 1

Evaluate the power

\frac{128}{3} \times i

Evaluate the power

More Steps

Evaluate

\frac{128}{3}

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

\frac{128}{3}

Simplify the radical expression

\frac{8 2}{3}

Multiply by the Conjugate

\frac{8 2 \times 3}{3 \times 3}

Multiply the numbers

\frac{8 6}{3 \times 3}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{8 6}{3}

\frac{8 6}{3} i

s = \pm \frac{8 6}{3} i

Separate the equation into 2 possible cases

s = \frac{8 6}{3} i s = - \frac{8 6}{3} i

Solution

s_{1} = - \frac{8 6}{3} i, s_{2} = \frac{8 6}{3} i

Alternative Form

s_{1} \approx - 6.531973 i, s_{2} \approx 6.531973 i

Show Solution