Solve 9x^2-16 - ScanMath

Question

Factor the expression

(3 x - 4) (3 x + 4)

Evaluate

9 x^{2} - 16

Rewrite the expression in exponential form

(3 x)^{2} - 4^{2}

Solution

(3 x - 4) (3 x + 4)

Show Solution

x_{1} = - \frac{4}{3}, x_{2} = \frac{4}{3}

Alternative Form

x_{1} = - 1. \dot{3}, x_{2} = 1. \dot{3}

Evaluate

9 x^{2} - 16

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

9 x^{2} - 16 = 0

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

9 x^{2} = 0 + 16

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

9 x^{2} = 16

Divide both sides

\frac{9 x ^{2}}{9} = \frac{16}{9}

Divide the numbers

x^{2} = \frac{16}{9}

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

x = \pm \frac{16}{9}

Simplify the expression

More Steps

Evaluate

\frac{16}{9}

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

\frac{16}{9}

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}{9}

Simplify the radical expression

More Steps

Evaluate

9

Write the number in exponential form with the base of 3

3^{2}

Reduce the index of the radical and exponent with 2

3

\frac{4}{3}

x = \pm \frac{4}{3}

Separate the equation into 2 possible cases

x = \frac{4}{3} x = - \frac{4}{3}

Solution

x_{1} = - \frac{4}{3}, x_{2} = \frac{4}{3}

Alternative Form

x_{1} = - 1. \dot{3}, x_{2} = 1. \dot{3}

Show Solution