Solve 9t^2-4 - ScanMath

Question

Factor the expression

(3 t - 2) (3 t + 2)

Evaluate

9 t^{2} - 4

Rewrite the expression in exponential form

(3 t)^{2} - 2^{2}

Solution

(3 t - 2) (3 t + 2)

Show Solution

t_{1} = - \frac{2}{3}, t_{2} = \frac{2}{3}

Alternative Form

t_{1} = - 0. \dot{6}, t_{2} = 0. \dot{6}

Evaluate

9 t^{2} - 4

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

9 t^{2} - 4 = 0

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

9 t^{2} = 0 + 4

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

9 t^{2} = 4

Divide both sides

\frac{9 t ^{2}}{9} = \frac{4}{9}

Divide the numbers

t^{2} = \frac{4}{9}

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

t = \pm \frac{4}{9}

Simplify the expression

More Steps

Evaluate

\frac{4}{9}

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

\frac{4}{9}

Simplify the radical expression

More Steps

Evaluate

4

Write the number in exponential form with the base of 2

2^{2}

Reduce the index of the radical and exponent with 2

2

\frac{2}{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{2}{3}

t = \pm \frac{2}{3}

Separate the equation into 2 possible cases

t = \frac{2}{3} t = - \frac{2}{3}

Solution

t_{1} = - \frac{2}{3}, t_{2} = \frac{2}{3}

Alternative Form

t_{1} = - 0. \dot{6}, t_{2} = 0. \dot{6}

Show Solution