Solve 2x^4-33x^2 100

Question

Simplify the expression

2 x^{4} - 3300 x^{2}

Evaluate

2 x^{4} - 33 x^{2} \times 100

Solution

2 x^{4} - 3300 x^{2}

Show Solution

2 x^{2} (x^{2} - 1650)

Evaluate

2 x^{4} - 33 x^{2} \times 100

Multiply the terms

2 x^{4} - 3300 x^{2}

Rewrite the expression

2 x^{2} \times x^{2} - 2 x^{2} \times 1650

Solution

2 x^{2} (x^{2} - 1650)

Show Solution

x_{1} = - 566, x_{2} = 0, x_{3} = 566

Alternative Form

x_{1} \approx - 40.620192, x_{2} = 0, x_{3} \approx 40.620192

Evaluate

2 x^{4} - 33 x^{2} \times 100

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

2 x^{4} - 33 x^{2} \times 100 = 0

Multiply the terms

2 x^{4} - 3300 x^{2} = 0

Factor the expression

2 x^{2} (x^{2} - 1650) = 0

Divide both sides

x^{2} (x^{2} - 1650) = 0

Separate the equation into 2 possible cases

x^{2} = 0 x^{2} - 1650 = 0

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

x = 0 x^{2} - 1650 = 0

Solve the equation

More Steps

Evaluate

x^{2} - 1650 = 0

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

x^{2} = 0 + 1650

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

x^{2} = 1650

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

x = \pm 1650

Simplify the expression

More Steps

Evaluate

1650

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

25 \times 66

Write the number in exponential form with the base of 5

5^{2} \times 66

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

5^{2} \times 66

Reduce the index of the radical and exponent with 2

566

x = \pm 566

Separate the equation into 2 possible cases

x = 566 x = - 566

x = 0 x = 566 x = - 566

Solution

x_{1} = - 566, x_{2} = 0, x_{3} = 566

Alternative Form

x_{1} \approx - 40.620192, x_{2} = 0, x_{3} \approx 40.620192

Show Solution