Solve x^4-13x^2 36

Question

Simplify the expression

x^{4} - 468 x^{2}

Evaluate

x^{4} - 13 x^{2} \times 36

Solution

x^{4} - 468 x^{2}

Show Solution

x^{2} (x^{2} - 468)

Evaluate

x^{4} - 13 x^{2} \times 36

Multiply the terms

x^{4} - 468 x^{2}

Rewrite the expression

x^{2} \times x^{2} - x^{2} \times 468

Solution

x^{2} (x^{2} - 468)

Show Solution

x_{1} = - 613, x_{2} = 0, x_{3} = 613

Alternative Form

x_{1} \approx - 21.633308, x_{2} = 0, x_{3} \approx 21.633308

Evaluate

x^{4} - 13 x^{2} \times 36

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

x^{4} - 13 x^{2} \times 36 = 0

Multiply the terms

x^{4} - 468 x^{2} = 0

Factor the expression

x^{2} (x^{2} - 468) = 0

Separate the equation into 2 possible cases

x^{2} = 0 x^{2} - 468 = 0

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

x = 0 x^{2} - 468 = 0

Solve the equation

More Steps

Evaluate

x^{2} - 468 = 0

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

x^{2} = 0 + 468

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

x^{2} = 468

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

x = \pm 468

Simplify the expression

More Steps

Evaluate

468

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

36 \times 13

Write the number in exponential form with the base of 6

6^{2} \times 13

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

6^{2} \times 13

Reduce the index of the radical and exponent with 2

613

x = \pm 613

Separate the equation into 2 possible cases

x = 613 x = - 613

x = 0 x = 613 x = - 613

Solution

x_{1} = - 613, x_{2} = 0, x_{3} = 613

Alternative Form

x_{1} \approx - 21.633308, x_{2} = 0, x_{3} \approx 21.633308

Show Solution