Solve c^44-9 - ScanMath

Question

Simplify the expression

4 c^{4} - 9

Evaluate

c^{4} \times 4 - 9

Solution

4 c^{4} - 9

Show Solution

(2 c^{2} - 3) (2 c^{2} + 3)

Evaluate

c^{4} \times 4 - 9

Use the commutative property to reorder the terms

4 c^{4} - 9

Rewrite the expression in exponential form

(2 c^{2})^{2} - 3^{2}

Solution

(2 c^{2} - 3) (2 c^{2} + 3)

Show Solution

c_{1} = - \frac{6}{2}, c_{2} = \frac{6}{2}

Alternative Form

c_{1} \approx - 1.224745, c_{2} \approx 1.224745

Evaluate

c^{4} \times 4 - 9

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

c^{4} \times 4 - 9 = 0

Use the commutative property to reorder the terms

4 c^{4} - 9 = 0

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

4 c^{4} = 0 + 9

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

4 c^{4} = 9

Divide both sides

\frac{4 c ^{4}}{4} = \frac{9}{4}

Divide the numbers

c^{4} = \frac{9}{4}

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

c = \pm 4 \frac{9}{4}

Simplify the expression

More Steps

Evaluate

4 \frac{9}{4}

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

\frac{4 9}{4 4}

Simplify the radical expression

More Steps

Evaluate

49

Write the number in exponential form with the base of 3

4 3^{2}

Reduce the index of the radical and exponent with 2

3

\frac{3}{4 4}

Simplify the radical expression

More Steps

Evaluate

44

Write the number in exponential form with the base of 2

4 2^{2}

Reduce the index of the radical and exponent with 2

2

\frac{3}{2}

Multiply by the Conjugate

\frac{3 \times 2}{2 \times 2}

Multiply the numbers

More Steps

Evaluate

3 \times 2

The product of roots with the same index is equal to the root of the product

3 \times 2

Calculate the product

6

\frac{6}{2 \times 2}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{6}{2}

c = \pm \frac{6}{2}

Separate the equation into 2 possible cases

c = \frac{6}{2} c = - \frac{6}{2}

Solution

c_{1} = - \frac{6}{2}, c_{2} = \frac{6}{2}

Alternative Form

c_{1} \approx - 1.224745, c_{2} \approx 1.224745

Show Solution