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Simplifying 26x2 + -22x = 180 Reorder the terms: -22x + 26x2 = 180 Solving -22x + 26x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + -22x + 26x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + -22x + 26x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-90 + -11x + 13x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-90 + -11x + 13x2)' equal to zero and attempt to solve: Simplifying -90 + -11x + 13x2 = 0 Solving -90 + -11x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -6.923076923 + -0.8461538462x + x2 = 0 Move the constant term to the right: Add '6.923076923' to each side of the equation. -6.923076923 + -0.8461538462x + 6.923076923 + x2 = 0 + 6.923076923 Reorder the terms: -6.923076923 + 6.923076923 + -0.8461538462x + x2 = 0 + 6.923076923 Combine like terms: -6.923076923 + 6.923076923 = 0.000000000 0.000000000 + -0.8461538462x + x2 = 0 + 6.923076923 -0.8461538462x + x2 = 0 + 6.923076923 Combine like terms: 0 + 6.923076923 = 6.923076923 -0.8461538462x + x2 = 6.923076923 The x term is -0.8461538462x. Take half its coefficient (-0.4230769231). Square it (0.1789940829) and add it to both sides. Add '0.1789940829' to each side of the equation. -0.8461538462x + 0.1789940829 + x2 = 6.923076923 + 0.1789940829 Reorder the terms: 0.1789940829 + -0.8461538462x + x2 = 6.923076923 + 0.1789940829 Combine like terms: 6.923076923 + 0.1789940829 = 7.1020710059 0.1789940829 + -0.8461538462x + x2 = 7.1020710059 Factor a perfect square on the left side: (x + -0.4230769231)(x + -0.4230769231) = 7.1020710059 Calculate the square root of the right side: 2.664971108 Break this problem into two subproblems by setting (x + -0.4230769231) equal to 2.664971108 and -2.664971108.Subproblem 1
x + -0.4230769231 = 2.664971108 Simplifying x + -0.4230769231 = 2.664971108 Reorder the terms: -0.4230769231 + x = 2.664971108 Solving -0.4230769231 + x = 2.664971108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4230769231' to each side of the equation. -0.4230769231 + 0.4230769231 + x = 2.664971108 + 0.4230769231 Combine like terms: -0.4230769231 + 0.4230769231 = 0.0000000000 0.0000000000 + x = 2.664971108 + 0.4230769231 x = 2.664971108 + 0.4230769231 Combine like terms: 2.664971108 + 0.4230769231 = 3.0880480311 x = 3.0880480311 Simplifying x = 3.0880480311Subproblem 2
x + -0.4230769231 = -2.664971108 Simplifying x + -0.4230769231 = -2.664971108 Reorder the terms: -0.4230769231 + x = -2.664971108 Solving -0.4230769231 + x = -2.664971108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4230769231' to each side of the equation. -0.4230769231 + 0.4230769231 + x = -2.664971108 + 0.4230769231 Combine like terms: -0.4230769231 + 0.4230769231 = 0.0000000000 0.0000000000 + x = -2.664971108 + 0.4230769231 x = -2.664971108 + 0.4230769231 Combine like terms: -2.664971108 + 0.4230769231 = -2.2418941849 x = -2.2418941849 Simplifying x = -2.2418941849Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.0880480311, -2.2418941849}Solution
x = {3.0880480311, -2.2418941849}
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