Solve 4m^2-9 - ScanMath

Question

Factor the expression

(2 m - 3) (2 m + 3)

Evaluate

4 m^{2} - 9

Rewrite the expression in exponential form

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

Solution

(2 m - 3) (2 m + 3)

Show Solution

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

Alternative Form

m_{1} = - 1.5, m_{2} = 1.5

Evaluate

4 m^{2} - 9

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

4 m^{2} - 9 = 0

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

4 m^{2} = 0 + 9

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

4 m^{2} = 9

Divide both sides

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

Divide the numbers

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

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

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

Simplify the expression

More Steps

Evaluate

\frac{9}{4}

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

\frac{9}{4}

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{3}{4}

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{3}{2}

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

Separate the equation into 2 possible cases

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

Solution

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

Alternative Form

m_{1} = - 1.5, m_{2} = 1.5

Show Solution