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Simplifying x(x + -35) + (x + -46) + 0.5x = 360 Reorder the terms: x(-35 + x) + (x + -46) + 0.5x = 360 (-35 * x + x * x) + (x + -46) + 0.5x = 360 (-35x + x2) + (x + -46) + 0.5x = 360 Reorder the terms: -35x + x2 + (-46 + x) + 0.5x = 360 Remove parenthesis around (-46 + x) -35x + x2 + -46 + x + 0.5x = 360 Reorder the terms: -46 + -35x + x + 0.5x + x2 = 360 Combine like terms: -35x + x = -34x -46 + -34x + 0.5x + x2 = 360 Combine like terms: -34x + 0.5x = -33.5x -46 + -33.5x + x2 = 360 Solving -46 + -33.5x + x2 = 360 Solving for variable 'x'. Reorder the terms: -46 + -360 + -33.5x + x2 = 360 + -360 Combine like terms: -46 + -360 = -406 -406 + -33.5x + x2 = 360 + -360 Combine like terms: 360 + -360 = 0 -406 + -33.5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '406' to each side of the equation. -406 + -33.5x + 406 + x2 = 0 + 406 Reorder the terms: -406 + 406 + -33.5x + x2 = 0 + 406 Combine like terms: -406 + 406 = 0 0 + -33.5x + x2 = 0 + 406 -33.5x + x2 = 0 + 406 Combine like terms: 0 + 406 = 406 -33.5x + x2 = 406 The x term is -33.5x. Take half its coefficient (-16.75). Square it (280.5625) and add it to both sides. Add '280.5625' to each side of the equation. -33.5x + 280.5625 + x2 = 406 + 280.5625 Reorder the terms: 280.5625 + -33.5x + x2 = 406 + 280.5625 Combine like terms: 406 + 280.5625 = 686.5625 280.5625 + -33.5x + x2 = 686.5625 Factor a perfect square on the left side: (x + -16.75)(x + -16.75) = 686.5625 Calculate the square root of the right side: 26.202337682 Break this problem into two subproblems by setting (x + -16.75) equal to 26.202337682 and -26.202337682.Subproblem 1
x + -16.75 = 26.202337682 Simplifying x + -16.75 = 26.202337682 Reorder the terms: -16.75 + x = 26.202337682 Solving -16.75 + x = 26.202337682 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.75' to each side of the equation. -16.75 + 16.75 + x = 26.202337682 + 16.75 Combine like terms: -16.75 + 16.75 = 0.00 0.00 + x = 26.202337682 + 16.75 x = 26.202337682 + 16.75 Combine like terms: 26.202337682 + 16.75 = 42.952337682 x = 42.952337682 Simplifying x = 42.952337682Subproblem 2
x + -16.75 = -26.202337682 Simplifying x + -16.75 = -26.202337682 Reorder the terms: -16.75 + x = -26.202337682 Solving -16.75 + x = -26.202337682 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.75' to each side of the equation. -16.75 + 16.75 + x = -26.202337682 + 16.75 Combine like terms: -16.75 + 16.75 = 0.00 0.00 + x = -26.202337682 + 16.75 x = -26.202337682 + 16.75 Combine like terms: -26.202337682 + 16.75 = -9.452337682 x = -9.452337682 Simplifying x = -9.452337682Solution
The solution to the problem is based on the solutions from the subproblems. x = {42.952337682, -9.452337682}
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