Solve -8c 10c-4 - ScanMath

Question

Simplify the expression

- 80 c^{2} - 4

Evaluate

- 8 c \times 10 c - 4

Solution

More Steps

Evaluate

- 8 c \times 10 c

Multiply the terms

- 80 c \times c

Multiply the terms

- 80 c^{2}

- 80 c^{2} - 4

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Factor the expression

- 4 (20 c^{2} + 1)

Evaluate

- 8 c \times 10 c - 4

Multiply

More Steps

Evaluate

- 8 c \times 10 c

Multiply the terms

- 80 c \times c

Multiply the terms

- 80 c^{2}

- 80 c^{2} - 4

Solution

- 4 (20 c^{2} + 1)

Show Solution

Find the roots

c_{1} = - \frac{5}{10} i, c_{2} = \frac{5}{10} i

Alternative Form

c_{1} \approx - 0.223607 i, c_{2} \approx 0.223607 i

Evaluate

- 8 c \times 10 c - 4

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

- 8 c \times 10 c - 4 = 0

Multiply

More Steps

Multiply the terms

- 8 c \times 10 c

Multiply the terms

- 80 c \times c

Multiply the terms

- 80 c^{2}

- 80 c^{2} - 4 = 0

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

- 80 c^{2} = 0 + 4

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

- 80 c^{2} = 4

Change the signs on both sides of the equation

80 c^{2} = - 4

Divide both sides

\frac{80 c ^{2}}{80} = \frac{- 4}{80}

Divide the numbers

c^{2} = \frac{- 4}{80}

Divide the numbers

More Steps

Evaluate

\frac{- 4}{80}

Cancel out the common factor 4

\frac{- 1}{20}

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

- \frac{1}{20}

c^{2} = - \frac{1}{20}

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

c = \pm - \frac{1}{20}

Simplify the expression

More Steps

Evaluate

- \frac{1}{20}

Evaluate the power

\frac{1}{20} \times - 1

Evaluate the power

\frac{1}{20} \times i

Evaluate the power

More Steps

Evaluate

\frac{1}{20}

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

\frac{1}{20}

Simplify the radical expression

\frac{1}{20}

Simplify the radical expression

\frac{1}{2 5}

Multiply by the Conjugate

\frac{5}{2 5 \times 5}

Multiply the numbers

\frac{5}{10}

\frac{5}{10} i

c = \pm \frac{5}{10} i

Separate the equation into 2 possible cases

c = \frac{5}{10} i c = - \frac{5}{10} i

Solution

c_{1} = - \frac{5}{10} i, c_{2} = \frac{5}{10} i

Alternative Form

c_{1} \approx - 0.223607 i, c_{2} \approx 0.223607 i

Show Solution