Solve 49h^2-16 - ScanMath

Question

Factor the expression

(7 h - 4) (7 h + 4)

Evaluate

49 h^{2} - 16

Rewrite the expression in exponential form

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

Solution

(7 h - 4) (7 h + 4)

Show Solution

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

Alternative Form

h_{1} = - 0. \dot{5} 7142 \dot{8}, h_{2} = 0. \dot{5} 7142 \dot{8}

Evaluate

49 h^{2} - 16

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

49 h^{2} - 16 = 0

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

49 h^{2} = 0 + 16

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

49 h^{2} = 16

Divide both sides

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

Divide the numbers

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

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

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

Simplify the expression

More Steps

Evaluate

\frac{16}{49}

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

\frac{16}{49}

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{4}{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{4}{7}

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

Separate the equation into 2 possible cases

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

Solution

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

Alternative Form

h_{1} = - 0. \dot{5} 7142 \dot{8}, h_{2} = 0. \dot{5} 7142 \dot{8}

Show Solution