Solve 144c^2-25 - ScanMath

Question

Factor the expression

(12 c - 5) (12 c + 5)

Evaluate

144 c^{2} - 25

Rewrite the expression in exponential form

(12 c)^{2} - 5^{2}

Solution

(12 c - 5) (12 c + 5)

Show Solution

c_{1} = - \frac{5}{12}, c_{2} = \frac{5}{12}

Alternative Form

c_{1} = - 0.41 \dot{6}, c_{2} = 0.41 \dot{6}

Evaluate

144 c^{2} - 25

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

144 c^{2} - 25 = 0

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

144 c^{2} = 0 + 25

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

144 c^{2} = 25

Divide both sides

\frac{144 c ^{2}}{144} = \frac{25}{144}

Divide the numbers

c^{2} = \frac{25}{144}

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

c = \pm \frac{25}{144}

Simplify the expression

More Steps

Evaluate

\frac{25}{144}

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

\frac{25}{144}

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{5}{144}

Simplify the radical expression

More Steps

Evaluate

144

Write the number in exponential form with the base of 12

1 2^{2}

Reduce the index of the radical and exponent with 2

12

\frac{5}{12}

c = \pm \frac{5}{12}

Separate the equation into 2 possible cases

c = \frac{5}{12} c = - \frac{5}{12}

Solution

c_{1} = - \frac{5}{12}, c_{2} = \frac{5}{12}

Alternative Form

c_{1} = - 0.41 \dot{6}, c_{2} = 0.41 \dot{6}

Show Solution