Solve 32x 1323 =3x^33

Question

Solve the equation

x_{1} = - 286, x_{2} = 0, x_{3} = 286

Alternative Form

x_{1} \approx - 68.585713, x_{2} = 0, x_{3} \approx 68.585713

Evaluate

32 x \times 1323 = 3 x^{3} \times 3

Multiply the terms

42336 x = 3 x^{3} \times 3

Multiply the terms

42336 x = 9 x^{3}

Add or subtract both sides

42336 x - 9 x^{3} = 0

Factor the expression

9 x (4704 - x^{2}) = 0

Divide both sides

x (4704 - x^{2}) = 0

Separate the equation into 2 possible cases

x = 0 4704 - x^{2} = 0

Solve the equation

More Steps

Evaluate

4704 - x^{2} = 0

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

- x^{2} = 0 - 4704

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

- x^{2} = - 4704

Change the signs on both sides of the equation

x^{2} = 4704

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

x = \pm 4704

Simplify the expression

More Steps

Evaluate

4704

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

784 \times 6

Write the number in exponential form with the base of 28

2 8^{2} \times 6

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

2 8^{2} \times 6

Reduce the index of the radical and exponent with 2

286

x = \pm 286

Separate the equation into 2 possible cases

x = 286 x = - 286

x = 0 x = 286 x = - 286

Solution

x_{1} = - 286, x_{2} = 0, x_{3} = 286

Alternative Form

x_{1} \approx - 68.585713, x_{2} = 0, x_{3} \approx 68.585713

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