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Simplifying 243x + 162 = 3x2 + -3x + -18 Reorder the terms: 162 + 243x = 3x2 + -3x + -18 Reorder the terms: 162 + 243x = -18 + -3x + 3x2 Solving 162 + 243x = -18 + -3x + 3x2 Solving for variable 'x'. Reorder the terms: 162 + 18 + 243x + 3x + -3x2 = -18 + -3x + 3x2 + 18 + 3x + -3x2 Combine like terms: 162 + 18 = 180 180 + 243x + 3x + -3x2 = -18 + -3x + 3x2 + 18 + 3x + -3x2 Combine like terms: 243x + 3x = 246x 180 + 246x + -3x2 = -18 + -3x + 3x2 + 18 + 3x + -3x2 Reorder the terms: 180 + 246x + -3x2 = -18 + 18 + -3x + 3x + 3x2 + -3x2 Combine like terms: -18 + 18 = 0 180 + 246x + -3x2 = 0 + -3x + 3x + 3x2 + -3x2 180 + 246x + -3x2 = -3x + 3x + 3x2 + -3x2 Combine like terms: -3x + 3x = 0 180 + 246x + -3x2 = 0 + 3x2 + -3x2 180 + 246x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 180 + 246x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(60 + 82x + -1x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(60 + 82x + -1x2)' equal to zero and attempt to solve: Simplifying 60 + 82x + -1x2 = 0 Solving 60 + 82x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -60 + -82x + x2 = 0 Move the constant term to the right: Add '60' to each side of the equation. -60 + -82x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + -82x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + -82x + x2 = 0 + 60 -82x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 -82x + x2 = 60 The x term is -82x. Take half its coefficient (-41). Square it (1681) and add it to both sides. Add '1681' to each side of the equation. -82x + 1681 + x2 = 60 + 1681 Reorder the terms: 1681 + -82x + x2 = 60 + 1681 Combine like terms: 60 + 1681 = 1741 1681 + -82x + x2 = 1741 Factor a perfect square on the left side: (x + -41)(x + -41) = 1741 Calculate the square root of the right side: 41.72529209 Break this problem into two subproblems by setting (x + -41) equal to 41.72529209 and -41.72529209.Subproblem 1
x + -41 = 41.72529209 Simplifying x + -41 = 41.72529209 Reorder the terms: -41 + x = 41.72529209 Solving -41 + x = 41.72529209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '41' to each side of the equation. -41 + 41 + x = 41.72529209 + 41 Combine like terms: -41 + 41 = 0 0 + x = 41.72529209 + 41 x = 41.72529209 + 41 Combine like terms: 41.72529209 + 41 = 82.72529209 x = 82.72529209 Simplifying x = 82.72529209Subproblem 2
x + -41 = -41.72529209 Simplifying x + -41 = -41.72529209 Reorder the terms: -41 + x = -41.72529209 Solving -41 + x = -41.72529209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '41' to each side of the equation. -41 + 41 + x = -41.72529209 + 41 Combine like terms: -41 + 41 = 0 0 + x = -41.72529209 + 41 x = -41.72529209 + 41 Combine like terms: -41.72529209 + 41 = -0.72529209 x = -0.72529209 Simplifying x = -0.72529209Solution
The solution to the problem is based on the solutions from the subproblems. x = {82.72529209, -0.72529209}Solution
x = {82.72529209, -0.72529209}
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