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Simplifying 36x2 + -476x + -2462 = 0 Reorder the terms: -2462 + -476x + 36x2 = 0 Solving -2462 + -476x + 36x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1231 + -238x + 18x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1231 + -238x + 18x2)' equal to zero and attempt to solve: Simplifying -1231 + -238x + 18x2 = 0 Solving -1231 + -238x + 18x2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -68.38888889 + -13.22222222x + x2 = 0 Move the constant term to the right: Add '68.38888889' to each side of the equation. -68.38888889 + -13.22222222x + 68.38888889 + x2 = 0 + 68.38888889 Reorder the terms: -68.38888889 + 68.38888889 + -13.22222222x + x2 = 0 + 68.38888889 Combine like terms: -68.38888889 + 68.38888889 = 0.00000000 0.00000000 + -13.22222222x + x2 = 0 + 68.38888889 -13.22222222x + x2 = 0 + 68.38888889 Combine like terms: 0 + 68.38888889 = 68.38888889 -13.22222222x + x2 = 68.38888889 The x term is -13.22222222x. Take half its coefficient (-6.61111111). Square it (43.70679011) and add it to both sides. Add '43.70679011' to each side of the equation. -13.22222222x + 43.70679011 + x2 = 68.38888889 + 43.70679011 Reorder the terms: 43.70679011 + -13.22222222x + x2 = 68.38888889 + 43.70679011 Combine like terms: 68.38888889 + 43.70679011 = 112.095679 43.70679011 + -13.22222222x + x2 = 112.095679 Factor a perfect square on the left side: (x + -6.61111111)(x + -6.61111111) = 112.095679 Calculate the square root of the right side: 10.587524687 Break this problem into two subproblems by setting (x + -6.61111111) equal to 10.587524687 and -10.587524687.Subproblem 1
x + -6.61111111 = 10.587524687 Simplifying x + -6.61111111 = 10.587524687 Reorder the terms: -6.61111111 + x = 10.587524687 Solving -6.61111111 + x = 10.587524687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.61111111' to each side of the equation. -6.61111111 + 6.61111111 + x = 10.587524687 + 6.61111111 Combine like terms: -6.61111111 + 6.61111111 = 0.00000000 0.00000000 + x = 10.587524687 + 6.61111111 x = 10.587524687 + 6.61111111 Combine like terms: 10.587524687 + 6.61111111 = 17.198635797 x = 17.198635797 Simplifying x = 17.198635797Subproblem 2
x + -6.61111111 = -10.587524687 Simplifying x + -6.61111111 = -10.587524687 Reorder the terms: -6.61111111 + x = -10.587524687 Solving -6.61111111 + x = -10.587524687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.61111111' to each side of the equation. -6.61111111 + 6.61111111 + x = -10.587524687 + 6.61111111 Combine like terms: -6.61111111 + 6.61111111 = 0.00000000 0.00000000 + x = -10.587524687 + 6.61111111 x = -10.587524687 + 6.61111111 Combine like terms: -10.587524687 + 6.61111111 = -3.976413577 x = -3.976413577 Simplifying x = -3.976413577Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.198635797, -3.976413577}Solution
x = {17.198635797, -3.976413577}
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