Solve 100r^2-4 - ScanMath

Question

Factor the expression

4 (5 r - 1) (5 r + 1)

Evaluate

100 r^{2} - 4

Factor out 4 from the expression

4 (25 r^{2} - 1)

Solution

More Steps

Evaluate

25 r^{2} - 1

Rewrite the expression in exponential form

(5 r)^{2} - 1^{2}

Use a^{2} - b^{2} = (a - b) (a + b) to factor the expression

(5 r - 1) (5 r + 1)

4 (5 r - 1) (5 r + 1)

Show Solution

r_{1} = - \frac{1}{5}, r_{2} = \frac{1}{5}

Alternative Form

r_{1} = - 0.2, r_{2} = 0.2

Evaluate

100 r^{2} - 4

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

100 r^{2} - 4 = 0

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

100 r^{2} = 0 + 4

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

100 r^{2} = 4

Divide both sides

\frac{100 r ^{2}}{100} = \frac{4}{100}

Divide the numbers

r^{2} = \frac{4}{100}

Cancel out the common factor 4

r^{2} = \frac{1}{25}

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

r = \pm \frac{1}{25}

Simplify the expression

More Steps

Evaluate

\frac{1}{25}

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

\frac{1}{25}

Simplify the radical expression

\frac{1}{25}

Simplify the radical expression

More Steps

Evaluate

25

Write the number in exponential form with the base of 5

5^{2}

Reduce the index of the radical and exponent with 2

5

\frac{1}{5}

r = \pm \frac{1}{5}

Separate the equation into 2 possible cases

r = \frac{1}{5} r = - \frac{1}{5}

Solution

r_{1} = - \frac{1}{5}, r_{2} = \frac{1}{5}

Alternative Form

r_{1} = - 0.2, r_{2} = 0.2

Show Solution