Solve 8x 72= 2x^36

Question

Solve the equation

x_{1} = - 43, x_{2} = 0, x_{3} = 43

Alternative Form

x_{1} \approx - 6.928203, x_{2} = 0, x_{3} \approx 6.928203

Evaluate

8 x \times 72 = 2 x^{3} \times 6

Multiply the terms

576 x = 2 x^{3} \times 6

Multiply the terms

576 x = 12 x^{3}

Add or subtract both sides

576 x - 12 x^{3} = 0

Factor the expression

12 x (48 - x^{2}) = 0

Divide both sides

x (48 - x^{2}) = 0

Separate the equation into 2 possible cases

x = 0 48 - x^{2} = 0

Solve the equation

More Steps

Evaluate

48 - x^{2} = 0

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

- x^{2} = 0 - 48

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

- x^{2} = - 48

Change the signs on both sides of the equation

x^{2} = 48

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

x = \pm 48

Simplify the expression

More Steps

Evaluate

48

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

16 \times 3

Write the number in exponential form with the base of 4

4^{2} \times 3

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

4^{2} \times 3

Reduce the index of the radical and exponent with 2

43

x = \pm 43

Separate the equation into 2 possible cases

x = 43 x = - 43

x = 0 x = 43 x = - 43

Solution

x_{1} = - 43, x_{2} = 0, x_{3} = 43

Alternative Form

x_{1} \approx - 6.928203, x_{2} = 0, x_{3} \approx 6.928203

Show Solution