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Simplifying 5x + x2 + -14 = 180 Reorder the terms: -14 + 5x + x2 = 180 Solving -14 + 5x + x2 = 180 Solving for variable 'x'. Reorder the terms: -14 + -180 + 5x + x2 = 180 + -180 Combine like terms: -14 + -180 = -194 -194 + 5x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -194 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '194' to each side of the equation. -194 + 5x + 194 + x2 = 0 + 194 Reorder the terms: -194 + 194 + 5x + x2 = 0 + 194 Combine like terms: -194 + 194 = 0 0 + 5x + x2 = 0 + 194 5x + x2 = 0 + 194 Combine like terms: 0 + 194 = 194 5x + x2 = 194 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 = 194 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 194 + 6.25 Combine like terms: 194 + 6.25 = 200.25 6.25 + 5x + x2 = 200.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 200.25 Calculate the square root of the right side: 14.150971698 Break this problem into two subproblems by setting (x + 2.5) equal to 14.150971698 and -14.150971698.Subproblem 1
x + 2.5 = 14.150971698 Simplifying x + 2.5 = 14.150971698 Reorder the terms: 2.5 + x = 14.150971698 Solving 2.5 + x = 14.150971698 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 = 14.150971698 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 14.150971698 + -2.5 x = 14.150971698 + -2.5 Combine like terms: 14.150971698 + -2.5 = 11.650971698 x = 11.650971698 Simplifying x = 11.650971698Subproblem 2
x + 2.5 = -14.150971698 Simplifying x + 2.5 = -14.150971698 Reorder the terms: 2.5 + x = -14.150971698 Solving 2.5 + x = -14.150971698 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 = -14.150971698 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -14.150971698 + -2.5 x = -14.150971698 + -2.5 Combine like terms: -14.150971698 + -2.5 = -16.650971698 x = -16.650971698 Simplifying x = -16.650971698Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.650971698, -16.650971698}
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