Solve 8n^2+65+8 - ScanMath

Question

Simplify the expression

8 n^{2} + 73

Evaluate

8 n^{2} + 65 + 8

Solution

8 n^{2} + 73

Show Solution

n_{1} = - \frac{146}{4} i, n_{2} = \frac{146}{4} i

Alternative Form

n_{1} \approx - 3.020761 i, n_{2} \approx 3.020761 i

Evaluate

8 n^{2} + 65 + 8

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

8 n^{2} + 65 + 8 = 0

Add the numbers

8 n^{2} + 73 = 0

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

8 n^{2} = 0 - 73

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

8 n^{2} = - 73

Divide both sides

\frac{8 n ^{2}}{8} = \frac{- 73}{8}

Divide the numbers

n^{2} = \frac{- 73}{8}

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

n^{2} = - \frac{73}{8}

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

n = \pm - \frac{73}{8}

Simplify the expression

More Steps

Evaluate

- \frac{73}{8}

Evaluate the power

\frac{73}{8} \times - 1

Evaluate the power

\frac{73}{8} \times i

Evaluate the power

More Steps

Evaluate

\frac{73}{8}

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

\frac{73}{8}

Simplify the radical expression

\frac{73}{2 2}

Multiply by the Conjugate

\frac{73 \times 2}{2 2 \times 2}

Multiply the numbers

\frac{146}{2 2 \times 2}

Multiply the numbers

\frac{146}{4}

\frac{146}{4} i

n = \pm \frac{146}{4} i

Separate the equation into 2 possible cases

n = \frac{146}{4} i n = - \frac{146}{4} i

Solution

n_{1} = - \frac{146}{4} i, n_{2} = \frac{146}{4} i

Alternative Form

n_{1} \approx - 3.020761 i, n_{2} \approx 3.020761 i

Show Solution