Solve 16-36/4x^2 - ScanMath

Question

Simplify the expression

16 - 9 x^{2}

Evaluate

16 - \frac{36}{4} x^{2}

Solution

More Steps

Evaluate

\frac{36}{4}

Reduce the numbers

\frac{9}{1}

Calculate

9

16 - 9 x^{2}

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Factor the expression

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

Evaluate

16 - \frac{36}{4} x^{2}

Evaluate

More Steps

Evaluate

\frac{36}{4} x^{2}

Divide the terms

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Evaluate

\frac{36}{4}

Reduce the numbers

\frac{9}{1}

Calculate

9

9 x^{2}

16 - 9 x^{2}

Rewrite the expression in exponential form

4^{2} - (3 x)^{2}

Solution

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

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Find the roots

x_{1} = - \frac{4}{3}, x_{2} = \frac{4}{3}

Alternative Form

x_{1} = - 1. \dot{3}, x_{2} = 1. \dot{3}

Evaluate

16 - \frac{36}{4} x^{2}

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

16 - \frac{36}{4} x^{2} = 0

Divide the terms

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Evaluate

\frac{36}{4}

Reduce the numbers

\frac{9}{1}

Calculate

9

16 - 9 x^{2} = 0

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

- 9 x^{2} = 0 - 16

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

- 9 x^{2} = - 16

Change the signs on both sides of the equation

9 x^{2} = 16

Divide both sides

\frac{9 x ^{2}}{9} = \frac{16}{9}

Divide the numbers

x^{2} = \frac{16}{9}

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

x = \pm \frac{16}{9}

Simplify the expression

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Evaluate

\frac{16}{9}

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

\frac{16}{9}

Simplify the radical expression

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Evaluate

16

Write the number in exponential form with the base of 4

4^{2}

Reduce the index of the radical and exponent with 2

4

\frac{4}{9}

Simplify the radical expression

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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{4}{3}

x = \pm \frac{4}{3}

Separate the equation into 2 possible cases

x = \frac{4}{3} x = - \frac{4}{3}

Solution

x_{1} = - \frac{4}{3}, x_{2} = \frac{4}{3}

Alternative Form

x_{1} = - 1. \dot{3}, x_{2} = 1. \dot{3}

Show Solution