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Simplifying x2 + 3x + -5 = 180 Reorder the terms: -5 + 3x + x2 = 180 Solving -5 + 3x + x2 = 180 Solving for variable 'x'. Reorder the terms: -5 + -180 + 3x + x2 = 180 + -180 Combine like terms: -5 + -180 = -185 -185 + 3x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -185 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '185' to each side of the equation. -185 + 3x + 185 + x2 = 0 + 185 Reorder the terms: -185 + 185 + 3x + x2 = 0 + 185 Combine like terms: -185 + 185 = 0 0 + 3x + x2 = 0 + 185 3x + x2 = 0 + 185 Combine like terms: 0 + 185 = 185 3x + x2 = 185 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 185 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 185 + 2.25 Combine like terms: 185 + 2.25 = 187.25 2.25 + 3x + x2 = 187.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 187.25 Calculate the square root of the right side: 13.683932183 Break this problem into two subproblems by setting (x + 1.5) equal to 13.683932183 and -13.683932183.Subproblem 1
x + 1.5 = 13.683932183 Simplifying x + 1.5 = 13.683932183 Reorder the terms: 1.5 + x = 13.683932183 Solving 1.5 + x = 13.683932183 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 13.683932183 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 13.683932183 + -1.5 x = 13.683932183 + -1.5 Combine like terms: 13.683932183 + -1.5 = 12.183932183 x = 12.183932183 Simplifying x = 12.183932183Subproblem 2
x + 1.5 = -13.683932183 Simplifying x + 1.5 = -13.683932183 Reorder the terms: 1.5 + x = -13.683932183 Solving 1.5 + x = -13.683932183 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -13.683932183 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -13.683932183 + -1.5 x = -13.683932183 + -1.5 Combine like terms: -13.683932183 + -1.5 = -15.183932183 x = -15.183932183 Simplifying x = -15.183932183Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.183932183, -15.183932183}
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