Solve n*n+1/2 - ScanMath

Question

Simplify the expression

n^{2} + \frac{1}{2}

Evaluate

n \times n + \frac{1}{2}

Solution

n^{2} + \frac{1}{2}

Show Solution

\frac{1}{2} (2 n^{2} + 1)

Evaluate

n \times n + \frac{1}{2}

Multiply the terms

n^{2} + \frac{1}{2}

Solution

\frac{1}{2} (2 n^{2} + 1)

Show Solution

n_{1} = - \frac{2}{2} i, n_{2} = \frac{2}{2} i

Alternative Form

n_{1} \approx - 0.707107 i, n_{2} \approx 0.707107 i

Evaluate

n \times n + \frac{1}{2}

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

n \times n + \frac{1}{2} = 0

Multiply the terms

n^{2} + \frac{1}{2} = 0

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

n^{2} = 0 - \frac{1}{2}

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

n^{2} = - \frac{1}{2}

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

n = \pm - \frac{1}{2}

Simplify the expression

More Steps

Evaluate

- \frac{1}{2}

Evaluate the power

\frac{1}{2} \times - 1

Evaluate the power

\frac{1}{2} \times i

Evaluate the power

More Steps

Evaluate

\frac{1}{2}

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

\frac{1}{2}

Simplify the radical expression

\frac{1}{2}

Multiply by the Conjugate

\frac{2}{2 \times 2}

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

\frac{2}{2}

\frac{2}{2} i

n = \pm \frac{2}{2} i

Separate the equation into 2 possible cases

n = \frac{2}{2} i n = - \frac{2}{2} i

Solution

n_{1} = - \frac{2}{2} i, n_{2} = \frac{2}{2} i

Alternative Form

n_{1} \approx - 0.707107 i, n_{2} \approx 0.707107 i

Show Solution