-144x^2+x^4+1=0

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Solution for -144x^2+x^4+1=0 equation:


Simplifying
-144x2 + x4 + 1 = 0

Reorder the terms:
1 + -144x2 + x4 = 0

Solving
1 + -144x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -144x2 + -1 + x4 = 0 + -1

Reorder the terms:
1 + -1 + -144x2 + x4 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -144x2 + x4 = 0 + -1
-144x2 + x4 = 0 + -1

Combine like terms: 0 + -1 = -1
-144x2 + x4 = -1

The x term is -144x2.  Take half its coefficient (-72).
Square it (5184) and add it to both sides.

Add '5184' to each side of the equation.
-144x2 + 5184 + x4 = -1 + 5184

Reorder the terms:
5184 + -144x2 + x4 = -1 + 5184

Combine like terms: -1 + 5184 = 5183
5184 + -144x2 + x4 = 5183

Factor a perfect square on the left side:
(x2 + -72)(x2 + -72) = 5183

Calculate the square root of the right side: 71.993055221

Break this problem into two subproblems by setting 
(x2 + -72) equal to 71.993055221 and -71.993055221.

Subproblem 1

x2 + -72 = 71.993055221 Simplifying x2 + -72 = 71.993055221 Reorder the terms: -72 + x2 = 71.993055221 Solving -72 + x2 = 71.993055221 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '72' to each side of the equation. -72 + 72 + x2 = 71.993055221 + 72 Combine like terms: -72 + 72 = 0 0 + x2 = 71.993055221 + 72 x2 = 71.993055221 + 72 Combine like terms: 71.993055221 + 72 = 143.993055221 x2 = 143.993055221 Simplifying x2 = 143.993055221 Take the square root of each side: x = {-11.999710631, 11.999710631}

Subproblem 2

x2 + -72 = -71.993055221 Simplifying x2 + -72 = -71.993055221 Reorder the terms: -72 + x2 = -71.993055221 Solving -72 + x2 = -71.993055221 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '72' to each side of the equation. -72 + 72 + x2 = -71.993055221 + 72 Combine like terms: -72 + 72 = 0 0 + x2 = -71.993055221 + 72 x2 = -71.993055221 + 72 Combine like terms: -71.993055221 + 72 = 0.006944779 x2 = 0.006944779 Simplifying x2 = 0.006944779 Take the square root of each side: x = {-0.083335341, 0.083335341}

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-11.999710631, 11.999710631, -0.083335341, 0.083335341}

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