Solve 16p^2-49 - ScanMath

Question

Factor the expression

(4 p - 7) (4 p + 7)

Evaluate

16 p^{2} - 49

Rewrite the expression in exponential form

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

Solution

(4 p - 7) (4 p + 7)

Show Solution

p_{1} = - \frac{7}{4}, p_{2} = \frac{7}{4}

Alternative Form

p_{1} = - 1.75, p_{2} = 1.75

Evaluate

16 p^{2} - 49

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

16 p^{2} - 49 = 0

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

16 p^{2} = 0 + 49

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

16 p^{2} = 49

Divide both sides

\frac{16 p ^{2}}{16} = \frac{49}{16}

Divide the numbers

p^{2} = \frac{49}{16}

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

p = \pm \frac{49}{16}

Simplify the expression

More Steps

Evaluate

\frac{49}{16}

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

\frac{49}{16}

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{7}{16}

Simplify the radical expression

More Steps

Evaluate

16

Write the number in exponential form with the base of 4

4^{2}

Reduce the index of the radical and exponent with 2

4

\frac{7}{4}

p = \pm \frac{7}{4}

Separate the equation into 2 possible cases

p = \frac{7}{4} p = - \frac{7}{4}

Solution

p_{1} = - \frac{7}{4}, p_{2} = \frac{7}{4}

Alternative Form

p_{1} = - 1.75, p_{2} = 1.75

Show Solution