Solve x^4-10x^29 - ScanMath

Question

Simplify the expression

x^{4} - 90 x^{2}

Evaluate

x^{4} - 10 x^{2} \times 9

Solution

x^{4} - 90 x^{2}

Show Solution

x^{2} (x^{2} - 90)

Evaluate

x^{4} - 10 x^{2} \times 9

Multiply the terms

x^{4} - 90 x^{2}

Rewrite the expression

x^{2} \times x^{2} - x^{2} \times 90

Solution

x^{2} (x^{2} - 90)

Show Solution

x_{1} = - 310, x_{2} = 0, x_{3} = 310

Alternative Form

x_{1} \approx - 9.486833, x_{2} = 0, x_{3} \approx 9.486833

Evaluate

x^{4} - 10 x^{2} \times 9

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

x^{4} - 10 x^{2} \times 9 = 0

Multiply the terms

x^{4} - 90 x^{2} = 0

Factor the expression

x^{2} (x^{2} - 90) = 0

Separate the equation into 2 possible cases

x^{2} = 0 x^{2} - 90 = 0

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

x = 0 x^{2} - 90 = 0

Solve the equation

More Steps

Evaluate

x^{2} - 90 = 0

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

x^{2} = 0 + 90

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

x^{2} = 90

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

x = \pm 90

Simplify the expression

More Steps

Evaluate

90

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

9 \times 10

Write the number in exponential form with the base of 3

3^{2} \times 10

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

3^{2} \times 10

Reduce the index of the radical and exponent with 2

310

x = \pm 310

Separate the equation into 2 possible cases

x = 310 x = - 310

x = 0 x = 310 x = - 310

Solution

x_{1} = - 310, x_{2} = 0, x_{3} = 310

Alternative Form

x_{1} \approx - 9.486833, x_{2} = 0, x_{3} \approx 9.486833

Show Solution