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Simplifying 232x = 90 + -900x2 Solving 232x = 90 + -900x2 Solving for variable 'x'. Reorder the terms: -90 + 232x + 900x2 = 90 + -900x2 + -90 + 900x2 Reorder the terms: -90 + 232x + 900x2 = 90 + -90 + -900x2 + 900x2 Combine like terms: 90 + -90 = 0 -90 + 232x + 900x2 = 0 + -900x2 + 900x2 -90 + 232x + 900x2 = -900x2 + 900x2 Combine like terms: -900x2 + 900x2 = 0 -90 + 232x + 900x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-45 + 116x + 450x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-45 + 116x + 450x2)' equal to zero and attempt to solve: Simplifying -45 + 116x + 450x2 = 0 Solving -45 + 116x + 450x2 = 0 Begin completing the square. Divide all terms by 450 the coefficient of the squared term: Divide each side by '450'. -0.1 + 0.2577777778x + x2 = 0.0 Move the constant term to the right: Add '0.1' to each side of the equation. -0.1 + 0.2577777778x + 0.1 + x2 = 0.0 + 0.1 Reorder the terms: -0.1 + 0.1 + 0.2577777778x + x2 = 0.0 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + 0.2577777778x + x2 = 0.0 + 0.1 0.2577777778x + x2 = 0.0 + 0.1 Combine like terms: 0.0 + 0.1 = 0.1 0.2577777778x + x2 = 0.1 The x term is 0.2577777778x. Take half its coefficient (0.1288888889). Square it (0.01661234568) and add it to both sides. Add '0.01661234568' to each side of the equation. 0.2577777778x + 0.01661234568 + x2 = 0.1 + 0.01661234568 Reorder the terms: 0.01661234568 + 0.2577777778x + x2 = 0.1 + 0.01661234568 Combine like terms: 0.1 + 0.01661234568 = 0.11661234568 0.01661234568 + 0.2577777778x + x2 = 0.11661234568 Factor a perfect square on the left side: (x + 0.1288888889)(x + 0.1288888889) = 0.11661234568 Calculate the square root of the right side: 0.341485498 Break this problem into two subproblems by setting (x + 0.1288888889) equal to 0.341485498 and -0.341485498.Subproblem 1
x + 0.1288888889 = 0.341485498 Simplifying x + 0.1288888889 = 0.341485498 Reorder the terms: 0.1288888889 + x = 0.341485498 Solving 0.1288888889 + x = 0.341485498 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1288888889' to each side of the equation. 0.1288888889 + -0.1288888889 + x = 0.341485498 + -0.1288888889 Combine like terms: 0.1288888889 + -0.1288888889 = 0.0000000000 0.0000000000 + x = 0.341485498 + -0.1288888889 x = 0.341485498 + -0.1288888889 Combine like terms: 0.341485498 + -0.1288888889 = 0.2125966091 x = 0.2125966091 Simplifying x = 0.2125966091Subproblem 2
x + 0.1288888889 = -0.341485498 Simplifying x + 0.1288888889 = -0.341485498 Reorder the terms: 0.1288888889 + x = -0.341485498 Solving 0.1288888889 + x = -0.341485498 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1288888889' to each side of the equation. 0.1288888889 + -0.1288888889 + x = -0.341485498 + -0.1288888889 Combine like terms: 0.1288888889 + -0.1288888889 = 0.0000000000 0.0000000000 + x = -0.341485498 + -0.1288888889 x = -0.341485498 + -0.1288888889 Combine like terms: -0.341485498 + -0.1288888889 = -0.4703743869 x = -0.4703743869 Simplifying x = -0.4703743869Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2125966091, -0.4703743869}Solution
x = {0.2125966091, -0.4703743869}
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