Solve 81-4x^2 - ScanMath

Question

Factor the expression

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

Evaluate

81 - 4 x^{2}

Rewrite the expression in exponential form

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

Solution

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

Show Solution

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

Alternative Form

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

Evaluate

81 - 4 x^{2}

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

81 - 4 x^{2} = 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

Change the signs on both sides of the equation

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