Solve 1^2c1-2^2c^23^2c^3

Question

Simplify the expression

c - 36 c^{5}

Evaluate

1^{2} \times c \times 1 - 2^{2} c^{2} \times 3^{2} c^{3}

1 raised to any power equals to 1

1 \times c \times 1 - 2^{2} c^{2} \times 3^{2} c^{3}

Multiply the terms

c - 2^{2} c^{2} \times 3^{2} c^{3}

Multiply

More Steps

Multiply the terms

2^{2} c^{2} \times 3^{2} c^{3}

Multiply the terms with the same base by adding their exponents

2^{2} c^{2 + 3} \times 3^{2}

Add the numbers

2^{2} c^{5} \times 3^{2}

Multiply the numbers

More Steps

Evaluate

2^{2} \times 3^{2}

Multiply the terms with equal exponents by multiplying their bases

(2 \times 3)^{2}

Multiply the numbers

6^{2}

6^{2} c^{5}

c - 6^{2} c^{5}

Solution

c - 36 c^{5}

Show Solution

Factor the expression

c (1 - 6 c^{2}) (1 + 6 c^{2})

Evaluate

1^{2} \times c \times 1 - 2^{2} c^{2} \times 3^{2} c^{3}

Evaluate

More Steps

Evaluate

1^{2} \times c \times 1

1 raised to any power equals to 1

1 \times c \times 1

Multiply the terms

c

c - 2^{2} c^{2} \times 3^{2} c^{3}

Evaluate

More Steps

Evaluate

2^{2} c^{2} \times 3^{2} c^{3}

Multiply the terms with the same base by adding their exponents

2^{2} c^{2 + 3} \times 3^{2}

Add the numbers

2^{2} c^{5} \times 3^{2}

Multiply the numbers

More Steps

Evaluate

2^{2} \times 3^{2}

Multiply the terms with equal exponents by multiplying their bases

(2 \times 3)^{2}

Multiply the numbers

6^{2}

6^{2} c^{5}

Evaluate the power

36 c^{5}

c - 36 c^{5}

Factor out c from the expression

c (1 - 36 c^{4})

Solution

More Steps

Evaluate

1 - 36 c^{4}

Rewrite the expression in exponential form

1^{2} - (6 c^{2})^{2}

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

(1 - 6 c^{2}) (1 + 6 c^{2})

c (1 - 6 c^{2}) (1 + 6 c^{2})

Show Solution

Find the roots

c_{1} = - \frac{6}{6}, c_{2} = 0, c_{3} = \frac{6}{6}

Alternative Form

c_{1} \approx - 0.408248, c_{2} = 0, c_{3} \approx 0.408248

Evaluate

1^{2} \times c \times 1 - 2^{2} c^{2} \times 3^{2} c^{3}

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

1^{2} \times c \times 1 - 2^{2} c^{2} \times 3^{2} c^{3} = 0

1 raised to any power equals to 1

1 \times c \times 1 - 2^{2} c^{2} \times 3^{2} c^{3} = 0

Multiply the terms

c - 2^{2} c^{2} \times 3^{2} c^{3} = 0

Multiply

More Steps

Multiply the terms

2^{2} c^{2} \times 3^{2} c^{3}

Multiply the terms with the same base by adding their exponents

2^{2} c^{2 + 3} \times 3^{2}

Add the numbers

2^{2} c^{5} \times 3^{2}

Multiply the numbers

More Steps

Evaluate

2^{2} \times 3^{2}

Multiply the terms with equal exponents by multiplying their bases

(2 \times 3)^{2}

Multiply the numbers

6^{2}

6^{2} c^{5}

c - 6^{2} c^{5} = 0

Evaluate the power

c - 36 c^{5} = 0

Factor the expression

c (1 - 36 c^{4}) = 0

Separate the equation into 2 possible cases

c = 0 1 - 36 c^{4} = 0

Solve the equation

More Steps

Evaluate

1 - 36 c^{4} = 0

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

- 36 c^{4} = 0 - 1

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

- 36 c^{4} = - 1

Change the signs on both sides of the equation

36 c^{4} = 1

Divide both sides

\frac{36 c ^{4}}{36} = \frac{1}{36}

Divide the numbers

c^{4} = \frac{1}{36}

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

c = \pm 4 \frac{1}{36}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{36}

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

\frac{4 1}{4 36}

Simplify the radical expression

\frac{1}{4 36}

Simplify the radical expression

\frac{1}{6}

Multiply by the Conjugate

\frac{6}{6 \times 6}

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

\frac{6}{6}

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

Separate the equation into 2 possible cases

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

c = 0 c = \frac{6}{6} c = - \frac{6}{6}

Solution

c_{1} = - \frac{6}{6}, c_{2} = 0, c_{3} = \frac{6}{6}

Alternative Form

c_{1} \approx - 0.408248, c_{2} = 0, c_{3} \approx 0.408248

Show Solution