Solve 16x^4 - 81 - ScanMath

Question

Factor the expression

(2 x - 3) (2 x + 3) (4 x^{2} + 9)

Evaluate

16 x^{4} - 81

Rewrite the expression in exponential form

(4 x^{2})^{2} - (8 1^{\frac{1}{2}})^{2}

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

(4 x^{2} - 8 1^{\frac{1}{2}}) (4 x^{2} + 8 1^{\frac{1}{2}})

Evaluate

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Evaluate

4 x^{2} - 8 1^{\frac{1}{2}}

Calculate

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Evaluate

- 8 1^{\frac{1}{2}}

Rewrite in exponential form

- (3^{4})^{\frac{1}{2}}

Multiply the exponents

- 3^{4 \times \frac{1}{2}}

Multiply the exponents

- 3^{2}

Evaluate the power

- 9

4 x^{2} - 9

(4 x^{2} - 9) (4 x^{2} + 8 1^{\frac{1}{2}})

Evaluate

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Evaluate

4 x^{2} + 8 1^{\frac{1}{2}}

Calculate

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Evaluate

8 1^{\frac{1}{2}}

Rewrite in exponential form

(3^{4})^{\frac{1}{2}}

Multiply the exponents

3^{4 \times \frac{1}{2}}

Multiply the exponents

3^{2}

Evaluate the power

9

4 x^{2} + 9

(4 x^{2} - 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)

(2 x - 3) (2 x + 3) (4 x^{2} + 9)

Show Solution

Find the roots

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

Alternative Form

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

Evaluate

16 x^{4} - 81

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

16 x^{4} - 81 = 0

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

16 x^{4} = 0 + 81

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

16 x^{4} = 81

Divide both sides

\frac{16 x ^{4}}{16} = \frac{81}{16}

Divide the numbers

x^{4} = \frac{81}{16}

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

x = \pm 4 \frac{81}{16}

Simplify the expression

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Evaluate

4 \frac{81}{16}

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

\frac{4 81}{4 16}

Simplify the radical expression

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Evaluate

481

Write the number in exponential form with the base of 3

4 3^{4}

Reduce the index of the radical and exponent with 4

3

\frac{3}{4 16}

Simplify the radical expression

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Evaluate

416

Write the number in exponential form with the base of 2

4 2^{4}

Reduce the index of the radical and exponent with 4

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