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Simplifying (5x + 2) + (x2) = 180 Reorder the terms: (2 + 5x) + (x2) = 180 Remove parenthesis around (2 + 5x) 2 + 5x + (x2) = 180 2 + 5x + x2 = 180 Solving 2 + 5x + x2 = 180 Solving for variable 'x'. Reorder the terms: 2 + -180 + 5x + x2 = 180 + -180 Combine like terms: 2 + -180 = -178 -178 + 5x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -178 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '178' to each side of the equation. -178 + 5x + 178 + x2 = 0 + 178 Reorder the terms: -178 + 178 + 5x + x2 = 0 + 178 Combine like terms: -178 + 178 = 0 0 + 5x + x2 = 0 + 178 5x + x2 = 0 + 178 Combine like terms: 0 + 178 = 178 5x + x2 = 178 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 178 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 178 + 6.25 Combine like terms: 178 + 6.25 = 184.25 6.25 + 5x + x2 = 184.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 184.25 Calculate the square root of the right side: 13.57387196 Break this problem into two subproblems by setting (x + 2.5) equal to 13.57387196 and -13.57387196.Subproblem 1
x + 2.5 = 13.57387196 Simplifying x + 2.5 = 13.57387196 Reorder the terms: 2.5 + x = 13.57387196 Solving 2.5 + x = 13.57387196 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 13.57387196 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 13.57387196 + -2.5 x = 13.57387196 + -2.5 Combine like terms: 13.57387196 + -2.5 = 11.07387196 x = 11.07387196 Simplifying x = 11.07387196Subproblem 2
x + 2.5 = -13.57387196 Simplifying x + 2.5 = -13.57387196 Reorder the terms: 2.5 + x = -13.57387196 Solving 2.5 + x = -13.57387196 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -13.57387196 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -13.57387196 + -2.5 x = -13.57387196 + -2.5 Combine like terms: -13.57387196 + -2.5 = -16.07387196 x = -16.07387196 Simplifying x = -16.07387196Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.07387196, -16.07387196}
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