Solve 121c^4-44c^2 4

Question

Simplify the expression

121 c^{4} - 176 c^{2}

Evaluate

121 c^{4} - 44 c^{2} \times 4

Solution

121 c^{4} - 176 c^{2}

Show Solution

11 c^{2} (11 c^{2} - 16)

Evaluate

121 c^{4} - 44 c^{2} \times 4

Multiply the terms

121 c^{4} - 176 c^{2}

Rewrite the expression

11 c^{2} \times 11 c^{2} - 11 c^{2} \times 16

Solution

11 c^{2} (11 c^{2} - 16)

Show Solution

c_{1} = - \frac{4 11}{11}, c_{2} = 0, c_{3} = \frac{4 11}{11}

Alternative Form

c_{1} \approx - 1.206045, c_{2} = 0, c_{3} \approx 1.206045

Evaluate

121 c^{4} - 44 c^{2} \times 4

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

121 c^{4} - 44 c^{2} \times 4 = 0

Multiply the terms

121 c^{4} - 176 c^{2} = 0

Factor the expression

11 c^{2} (11 c^{2} - 16) = 0

Divide both sides

c^{2} (11 c^{2} - 16) = 0

Separate the equation into 2 possible cases

c^{2} = 0 11 c^{2} - 16 = 0

The only way a power can be 0 is when the base equals 0

c = 0 11 c^{2} - 16 = 0

Solve the equation

More Steps

Evaluate

11 c^{2} - 16 = 0

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

11 c^{2} = 0 + 16

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

11 c^{2} = 16

Divide both sides

\frac{11 c ^{2}}{11} = \frac{16}{11}

Divide the numbers

c^{2} = \frac{16}{11}

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

c = \pm \frac{16}{11}

Simplify the expression

More Steps

Evaluate

\frac{16}{11}

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

\frac{16}{11}

Simplify the radical expression

\frac{4}{11}

Multiply by the Conjugate

\frac{4 11}{11 \times 11}

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

\frac{4 11}{11}

c = \pm \frac{4 11}{11}

Separate the equation into 2 possible cases

c = \frac{4 11}{11} c = - \frac{4 11}{11}

c = 0 c = \frac{4 11}{11} c = - \frac{4 11}{11}

Solution

c_{1} = - \frac{4 11}{11}, c_{2} = 0, c_{3} = \frac{4 11}{11}

Alternative Form

c_{1} \approx - 1.206045, c_{2} = 0, c_{3} \approx 1.206045

Show Solution