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Simplifying x2 + 3x + -60 + 17x + -30 = 180 Reorder the terms: -60 + -30 + 3x + 17x + x2 = 180 Combine like terms: -60 + -30 = -90 -90 + 3x + 17x + x2 = 180 Combine like terms: 3x + 17x = 20x -90 + 20x + x2 = 180 Solving -90 + 20x + x2 = 180 Solving for variable 'x'. Reorder the terms: -90 + -180 + 20x + x2 = 180 + -180 Combine like terms: -90 + -180 = -270 -270 + 20x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -270 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '270' to each side of the equation. -270 + 20x + 270 + x2 = 0 + 270 Reorder the terms: -270 + 270 + 20x + x2 = 0 + 270 Combine like terms: -270 + 270 = 0 0 + 20x + x2 = 0 + 270 20x + x2 = 0 + 270 Combine like terms: 0 + 270 = 270 20x + x2 = 270 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 270 + 100 Reorder the terms: 100 + 20x + x2 = 270 + 100 Combine like terms: 270 + 100 = 370 100 + 20x + x2 = 370 Factor a perfect square on the left side: (x + 10)(x + 10) = 370 Calculate the square root of the right side: 19.235384062 Break this problem into two subproblems by setting (x + 10) equal to 19.235384062 and -19.235384062.Subproblem 1
x + 10 = 19.235384062 Simplifying x + 10 = 19.235384062 Reorder the terms: 10 + x = 19.235384062 Solving 10 + x = 19.235384062 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 19.235384062 + -10 Combine like terms: 10 + -10 = 0 0 + x = 19.235384062 + -10 x = 19.235384062 + -10 Combine like terms: 19.235384062 + -10 = 9.235384062 x = 9.235384062 Simplifying x = 9.235384062Subproblem 2
x + 10 = -19.235384062 Simplifying x + 10 = -19.235384062 Reorder the terms: 10 + x = -19.235384062 Solving 10 + x = -19.235384062 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -19.235384062 + -10 Combine like terms: 10 + -10 = 0 0 + x = -19.235384062 + -10 x = -19.235384062 + -10 Combine like terms: -19.235384062 + -10 = -29.235384062 x = -29.235384062 Simplifying x = -29.235384062Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.235384062, -29.235384062}
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