x^4-37x^2=-96

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Solution for x^4-37x^2=-96 equation:


Simplifying
x4 + -37x2 = -96

Reorder the terms:
-37x2 + x4 = -96

Solving
-37x2 + x4 = -96

Solving for variable 'x'.

Reorder the terms:
96 + -37x2 + x4 = -96 + 96

Combine like terms: -96 + 96 = 0
96 + -37x2 + x4 = 0

Begin completing the square.

Move the constant term to the right:

Add '-96' to each side of the equation.
96 + -37x2 + -96 + x4 = 0 + -96

Reorder the terms:
96 + -96 + -37x2 + x4 = 0 + -96

Combine like terms: 96 + -96 = 0
0 + -37x2 + x4 = 0 + -96
-37x2 + x4 = 0 + -96

Combine like terms: 0 + -96 = -96
-37x2 + x4 = -96

The x term is -37x2.  Take half its coefficient (-18.5).
Square it (342.25) and add it to both sides.

Add '342.25' to each side of the equation.
-37x2 + 342.25 + x4 = -96 + 342.25

Reorder the terms:
342.25 + -37x2 + x4 = -96 + 342.25

Combine like terms: -96 + 342.25 = 246.25
342.25 + -37x2 + x4 = 246.25

Factor a perfect square on the left side:
(x2 + -18.5)(x2 + -18.5) = 246.25

Calculate the square root of the right side: 15.692354826

Break this problem into two subproblems by setting 
(x2 + -18.5) equal to 15.692354826 and -15.692354826.

Subproblem 1

x2 + -18.5 = 15.692354826 Simplifying x2 + -18.5 = 15.692354826 Reorder the terms: -18.5 + x2 = 15.692354826 Solving -18.5 + x2 = 15.692354826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.5' to each side of the equation. -18.5 + 18.5 + x2 = 15.692354826 + 18.5 Combine like terms: -18.5 + 18.5 = 0.0 0.0 + x2 = 15.692354826 + 18.5 x2 = 15.692354826 + 18.5 Combine like terms: 15.692354826 + 18.5 = 34.192354826 x2 = 34.192354826 Simplifying x2 = 34.192354826 Take the square root of each side: x = {-5.847422922, 5.847422922}

Subproblem 2

x2 + -18.5 = -15.692354826 Simplifying x2 + -18.5 = -15.692354826 Reorder the terms: -18.5 + x2 = -15.692354826 Solving -18.5 + x2 = -15.692354826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.5' to each side of the equation. -18.5 + 18.5 + x2 = -15.692354826 + 18.5 Combine like terms: -18.5 + 18.5 = 0.0 0.0 + x2 = -15.692354826 + 18.5 x2 = -15.692354826 + 18.5 Combine like terms: -15.692354826 + 18.5 = 2.807645174 x2 = 2.807645174 Simplifying x2 = 2.807645174 Take the square root of each side: x = {-1.675602929, 1.675602929}

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-5.847422922, 5.847422922, -1.675602929, 1.675602929}

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