Solve 36x^2-81 - ScanMath

Question

Factor the expression

9 (2 x - 3) (2 x + 3)

Evaluate

36 x^{2} - 81

Factor out 9 from the expression

9 (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)

9 (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

36 x^{2} - 81

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

36 x^{2} - 81 = 0

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

36 x^{2} = 0 + 81

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

36 x^{2} = 81

Divide both sides

\frac{36 x ^{2}}{36} = \frac{81}{36}

Divide the numbers

x^{2} = \frac{81}{36}

Cancel out the common factor 9

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