2x^2+x^4=9

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Solution for 2x^2+x^4=9 equation:


Simplifying
2x2 + x4 = 9

Solving
2x2 + x4 = 9

Solving for variable 'x'.

Reorder the terms:
-9 + 2x2 + x4 = 9 + -9

Combine like terms: 9 + -9 = 0
-9 + 2x2 + x4 = 0

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + 2x2 + 9 + x4 = 0 + 9

Reorder the terms:
-9 + 9 + 2x2 + x4 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 2x2 + x4 = 0 + 9
2x2 + x4 = 0 + 9

Combine like terms: 0 + 9 = 9
2x2 + x4 = 9

The x term is 2x2.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x2 + 1 + x4 = 9 + 1

Reorder the terms:
1 + 2x2 + x4 = 9 + 1

Combine like terms: 9 + 1 = 10
1 + 2x2 + x4 = 10

Factor a perfect square on the left side:
(x2 + 1)(x2 + 1) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(x2 + 1) equal to 3.16227766 and -3.16227766.

Subproblem 1

x2 + 1 = 3.16227766 Simplifying x2 + 1 = 3.16227766 Reorder the terms: 1 + x2 = 3.16227766 Solving 1 + x2 = 3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x2 = 3.16227766 + -1 Combine like terms: 1 + -1 = 0 0 + x2 = 3.16227766 + -1 x2 = 3.16227766 + -1 Combine like terms: 3.16227766 + -1 = 2.16227766 x2 = 2.16227766 Simplifying x2 = 2.16227766 Take the square root of each side: x = {-1.470468517, 1.470468517}

Subproblem 2

x2 + 1 = -3.16227766 Simplifying x2 + 1 = -3.16227766 Reorder the terms: 1 + x2 = -3.16227766 Solving 1 + x2 = -3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x2 = -3.16227766 + -1 Combine like terms: 1 + -1 = 0 0 + x2 = -3.16227766 + -1 x2 = -3.16227766 + -1 Combine like terms: -3.16227766 + -1 = -4.16227766 x2 = -4.16227766 Simplifying x2 = -4.16227766 Reorder the terms: 4.16227766 + x2 = -4.16227766 + 4.16227766 Combine like terms: -4.16227766 + 4.16227766 = 0.00000000 4.16227766 + x2 = 0.00000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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