Solve 49p^2-36 - ScanMath

Question

Factor the expression

(7 p - 6) (7 p + 6)

Evaluate

49 p^{2} - 36

Rewrite the expression in exponential form

(7 p)^{2} - 6^{2}

Solution

(7 p - 6) (7 p + 6)

Show Solution

p_{1} = - \frac{6}{7}, p_{2} = \frac{6}{7}

Alternative Form

p_{1} = - 0. \dot{8} 5714 \dot{2}, p_{2} = 0. \dot{8} 5714 \dot{2}

Evaluate

49 p^{2} - 36

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

49 p^{2} - 36 = 0

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

49 p^{2} = 0 + 36

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

49 p^{2} = 36

Divide both sides

\frac{49 p ^{2}}{49} = \frac{36}{49}

Divide the numbers

p^{2} = \frac{36}{49}

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

p = \pm \frac{36}{49}

Simplify the expression

More Steps

Evaluate

\frac{36}{49}

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

\frac{36}{49}

Simplify the radical expression

More Steps

Evaluate

36

Write the number in exponential form with the base of 6

6^{2}

Reduce the index of the radical and exponent with 2

6

\frac{6}{49}

Simplify the radical expression

More Steps

Evaluate

49

Write the number in exponential form with the base of 7

7^{2}

Reduce the index of the radical and exponent with 2

7

\frac{6}{7}

p = \pm \frac{6}{7}

Separate the equation into 2 possible cases

p = \frac{6}{7} p = - \frac{6}{7}

Solution

p_{1} = - \frac{6}{7}, p_{2} = \frac{6}{7}

Alternative Form

p_{1} = - 0. \dot{8} 5714 \dot{2}, p_{2} = 0. \dot{8} 5714 \dot{2}

Show Solution