-49+37x^2-x^4=0

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Solution for -49+37x^2-x^4=0 equation:


Simplifying
-49 + 37x2 + -1x4 = 0

Solving
-49 + 37x2 + -1x4 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
49 + -37x2 + x4 = 0

Move the constant term to the right:

Add '-49' to each side of the equation.
49 + -37x2 + -49 + x4 = 0 + -49

Reorder the terms:
49 + -49 + -37x2 + x4 = 0 + -49

Combine like terms: 49 + -49 = 0
0 + -37x2 + x4 = 0 + -49
-37x2 + x4 = 0 + -49

Combine like terms: 0 + -49 = -49
-37x2 + x4 = -49

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 = -49 + 342.25

Reorder the terms:
342.25 + -37x2 + x4 = -49 + 342.25

Combine like terms: -49 + 342.25 = 293.25
342.25 + -37x2 + x4 = 293.25

Factor a perfect square on the left side:
(x2 + -18.5)(x2 + -18.5) = 293.25

Calculate the square root of the right side: 17.12454379

Break this problem into two subproblems by setting 
(x2 + -18.5) equal to 17.12454379 and -17.12454379.

Subproblem 1

x2 + -18.5 = 17.12454379 Simplifying x2 + -18.5 = 17.12454379 Reorder the terms: -18.5 + x2 = 17.12454379 Solving -18.5 + x2 = 17.12454379 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 = 17.12454379 + 18.5 Combine like terms: -18.5 + 18.5 = 0.0 0.0 + x2 = 17.12454379 + 18.5 x2 = 17.12454379 + 18.5 Combine like terms: 17.12454379 + 18.5 = 35.62454379 x2 = 35.62454379 Simplifying x2 = 35.62454379 Take the square root of each side: x = {-5.968629976, 5.968629976}

Subproblem 2

x2 + -18.5 = -17.12454379 Simplifying x2 + -18.5 = -17.12454379 Reorder the terms: -18.5 + x2 = -17.12454379 Solving -18.5 + x2 = -17.12454379 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 = -17.12454379 + 18.5 Combine like terms: -18.5 + 18.5 = 0.0 0.0 + x2 = -17.12454379 + 18.5 x2 = -17.12454379 + 18.5 Combine like terms: -17.12454379 + 18.5 = 1.37545621 x2 = 1.37545621 Simplifying x2 = 1.37545621 Take the square root of each side: x = {-1.172798452, 1.172798452}

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-5.968629976, 5.968629976, -1.172798452, 1.172798452}

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