Solve 4(3 c) c=c^4

Question

Solve the equation

c_{1} = - 23, c_{2} = 0, c_{3} = 23

Alternative Form

c_{1} \approx - 3.464102, c_{2} = 0, c_{3} \approx 3.464102

Evaluate

4 \times 3 c \times c = c^{4}

Multiply

More Steps

Evaluate

4 \times 3 c \times c

Multiply the terms

12 c \times c

Multiply the terms

12 c^{2}

12 c^{2} = c^{4}

Move the expression to the left side

12 c^{2} - c^{4} = 0

Factor the expression

c^{2} (12 - c^{2}) = 0

Separate the equation into 2 possible cases

c^{2} = 0 12 - c^{2} = 0

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

c = 0 12 - c^{2} = 0

Solve the equation

More Steps

Evaluate

12 - c^{2} = 0

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

- c^{2} = 0 - 12

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

- c^{2} = - 12

Change the signs on both sides of the equation

c^{2} = 12

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

c = \pm 12

Simplify the expression

More Steps

Evaluate

12

Write the expression as a product where the root of one of the factors can be evaluated

4 \times 3

Write the number in exponential form with the base of 2

2^{2} \times 3

The root of a product is equal to the product of the roots of each factor

2^{2} \times 3

Reduce the index of the radical and exponent with 2

23

c = \pm 23

Separate the equation into 2 possible cases

c = 23 c = - 23

c = 0 c = 23 c = - 23

Solution

c_{1} = - 23, c_{2} = 0, c_{3} = 23

Alternative Form

c_{1} \approx - 3.464102, c_{2} = 0, c_{3} \approx 3.464102

Show Solution