Solve 4-2(4c) 2(5c)

Question

Simplify the expression

4 - 80 c^{2}

Evaluate

4 - 2 \times 4 c \times 2 \times 5 c

Solution

More Steps

Evaluate

2 \times 4 c \times 2 \times 5 c

Multiply the terms

More Steps

Evaluate

2 \times 4 \times 2 \times 5

Multiply the terms

8 \times 2 \times 5

Multiply the terms

16 \times 5

Multiply the numbers

80

80 c \times c

Multiply the terms

80 c^{2}

4 - 80 c^{2}

Show Solution

Factor the expression

4 (1 - 20 c^{2})

Evaluate

4 - 2 \times 4 c \times 2 \times 5 c

Multiply

More Steps

Evaluate

2 \times 4 c \times 2 \times 5 c

Multiply the terms

More Steps

Evaluate

2 \times 4 \times 2 \times 5

Multiply the terms

8 \times 2 \times 5

Multiply the terms

16 \times 5

Multiply the numbers

80

80 c \times c

Multiply the terms

80 c^{2}

4 - 80 c^{2}

Solution

4 (1 - 20 c^{2})

Show Solution

Find the roots

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

Alternative Form

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

Evaluate

4 - 2 (4 c) \times 2 (5 c)

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

4 - 2 (4 c) \times 2 (5 c) = 0

Multiply the terms

4 - 2 \times 4 c \times 2 (5 c) = 0

Multiply the terms

4 - 2 \times 4 c \times 2 \times 5 c = 0

Multiply

More Steps

Multiply the terms

2 \times 4 c \times 2 \times 5 c

Multiply the terms

More Steps

Evaluate

2 \times 4 \times 2 \times 5

Multiply the terms

8 \times 2 \times 5

Multiply the terms

16 \times 5

Multiply the numbers

80

80 c \times c

Multiply the terms

80 c^{2}

4 - 80 c^{2} = 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}

Cancel out the common factor 4

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}

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

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Evaluate

20

Write the expression as a product where the root of one of the factors can be evaluated

4 \times 5

Write the number in exponential form with the base of 2

2^{2} \times 5

The root of a product is equal to the product of the roots of each factor

2^{2} \times 5

Reduce the index of the radical and exponent with 2

25

\frac{1}{2 5}

Multiply by the Conjugate

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

Multiply the numbers

More Steps

Evaluate

25 \times 5

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

2 \times 5

Multiply the terms

10

\frac{5}{10}

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

Separate the equation into 2 possible cases

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

Solution

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

Alternative Form

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

Show Solution