Solve 4x^2-81 - ScanMath

Question

Factor the expression

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

Evaluate

4 x^{2} - 81

Rewrite the expression in exponential form

(2 x)^{2} - 9^{2}

Solution

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

Show Solution

x_{1} = - \frac{9}{2}, x_{2} = \frac{9}{2}

Alternative Form

x_{1} = - 4.5, x_{2} = 4.5

Evaluate

4 x^{2} - 81

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

4 x^{2} - 81 = 0

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

4 x^{2} = 0 + 81

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

4 x^{2} = 81

Divide both sides

\frac{4 x ^{2}}{4} = \frac{81}{4}

Divide the numbers

x^{2} = \frac{81}{4}

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

x = \pm \frac{81}{4}

Simplify the expression

More Steps

Evaluate

\frac{81}{4}

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

\frac{81}{4}

Simplify the radical expression

More Steps

Evaluate

81

Write the number in exponential form with the base of 9

9^{2}

Reduce the index of the radical and exponent with 2

9

\frac{9}{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{9}{2}

x = \pm \frac{9}{2}

Separate the equation into 2 possible cases

x = \frac{9}{2} x = - \frac{9}{2}

Solution

x_{1} = - \frac{9}{2}, x_{2} = \frac{9}{2}

Alternative Form

x_{1} = - 4.5, x_{2} = 4.5

Show Solution