Solve x^4-20x^2 240

Question

Simplify the expression

x^{4} - 4800 x^{2}

Evaluate

x^{4} - 20 x^{2} \times 240

Solution

x^{4} - 4800 x^{2}

Show Solution

x^{2} (x^{2} - 4800)

Evaluate

x^{4} - 20 x^{2} \times 240

Multiply the terms

x^{4} - 4800 x^{2}

Rewrite the expression

x^{2} \times x^{2} - x^{2} \times 4800

Solution

x^{2} (x^{2} - 4800)

Show Solution

x_{1} = - 403, x_{2} = 0, x_{3} = 403

Alternative Form

x_{1} \approx - 69.282032, x_{2} = 0, x_{3} \approx 69.282032

Evaluate

x^{4} - 20 x^{2} \times 240

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

x^{4} - 20 x^{2} \times 240 = 0

Multiply the terms

x^{4} - 4800 x^{2} = 0

Factor the expression

x^{2} (x^{2} - 4800) = 0

Separate the equation into 2 possible cases

x^{2} = 0 x^{2} - 4800 = 0

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

x = 0 x^{2} - 4800 = 0

Solve the equation

More Steps

Evaluate

x^{2} - 4800 = 0

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

x^{2} = 0 + 4800

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

x^{2} = 4800

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

x = \pm 4800

Simplify the expression

More Steps

Evaluate

4800

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

1600 \times 3

Write the number in exponential form with the base of 40

4 0^{2} \times 3

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

4 0^{2} \times 3

Reduce the index of the radical and exponent with 2

403

x = \pm 403

Separate the equation into 2 possible cases

x = 403 x = - 403

x = 0 x = 403 x = - 403

Solution

x_{1} = - 403, x_{2} = 0, x_{3} = 403

Alternative Form

x_{1} \approx - 69.282032, x_{2} = 0, x_{3} \approx 69.282032

Show Solution