Solve 16x^(2 )- 36

Question

Factor the expression

4 (2 x - 3) (2 x + 3)

Evaluate

16 x^{2} - 36

Factor out 4 from the expression

4 (4 x^{2} - 9)

Solution

More Steps

Evaluate

4 x^{2} - 9

Rewrite the expression in exponential form

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

Use a^{2} - b^{2} = (a - b) (a + b) to factor the expression

(2 x - 3) (2 x + 3)

4 (2 x - 3) (2 x + 3)

Show Solution

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

Alternative Form

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

Evaluate

16 x^{2} - 36

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

16 x^{2} - 36 = 0

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

16 x^{2} = 0 + 36

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

16 x^{2} = 36

Divide both sides

\frac{16 x ^{2}}{16} = \frac{36}{16}

Divide the numbers

x^{2} = \frac{36}{16}

Cancel out the common factor 4

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

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

x = \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}

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

Separate the equation into 2 possible cases

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

Solution

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

Alternative Form

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

Show Solution