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Simplifying 8x2 + -40x + -50 = 5x2 + -35 Reorder the terms: -50 + -40x + 8x2 = 5x2 + -35 Reorder the terms: -50 + -40x + 8x2 = -35 + 5x2 Solving -50 + -40x + 8x2 = -35 + 5x2 Solving for variable 'x'. Reorder the terms: -50 + 35 + -40x + 8x2 + -5x2 = -35 + 5x2 + 35 + -5x2 Combine like terms: -50 + 35 = -15 -15 + -40x + 8x2 + -5x2 = -35 + 5x2 + 35 + -5x2 Combine like terms: 8x2 + -5x2 = 3x2 -15 + -40x + 3x2 = -35 + 5x2 + 35 + -5x2 Reorder the terms: -15 + -40x + 3x2 = -35 + 35 + 5x2 + -5x2 Combine like terms: -35 + 35 = 0 -15 + -40x + 3x2 = 0 + 5x2 + -5x2 -15 + -40x + 3x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -15 + -40x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -5 + -13.33333333x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -13.33333333x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -13.33333333x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -13.33333333x + x2 = 0 + 5 -13.33333333x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -13.33333333x + x2 = 5 The x term is -13.33333333x. Take half its coefficient (-6.666666665). Square it (44.44444442) and add it to both sides. Add '44.44444442' to each side of the equation. -13.33333333x + 44.44444442 + x2 = 5 + 44.44444442 Reorder the terms: 44.44444442 + -13.33333333x + x2 = 5 + 44.44444442 Combine like terms: 5 + 44.44444442 = 49.44444442 44.44444442 + -13.33333333x + x2 = 49.44444442 Factor a perfect square on the left side: (x + -6.666666665)(x + -6.666666665) = 49.44444442 Calculate the square root of the right side: 7.031674368 Break this problem into two subproblems by setting (x + -6.666666665) equal to 7.031674368 and -7.031674368.Subproblem 1
x + -6.666666665 = 7.031674368 Simplifying x + -6.666666665 = 7.031674368 Reorder the terms: -6.666666665 + x = 7.031674368 Solving -6.666666665 + x = 7.031674368 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.666666665' to each side of the equation. -6.666666665 + 6.666666665 + x = 7.031674368 + 6.666666665 Combine like terms: -6.666666665 + 6.666666665 = 0.000000000 0.000000000 + x = 7.031674368 + 6.666666665 x = 7.031674368 + 6.666666665 Combine like terms: 7.031674368 + 6.666666665 = 13.698341033 x = 13.698341033 Simplifying x = 13.698341033Subproblem 2
x + -6.666666665 = -7.031674368 Simplifying x + -6.666666665 = -7.031674368 Reorder the terms: -6.666666665 + x = -7.031674368 Solving -6.666666665 + x = -7.031674368 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.666666665' to each side of the equation. -6.666666665 + 6.666666665 + x = -7.031674368 + 6.666666665 Combine like terms: -6.666666665 + 6.666666665 = 0.000000000 0.000000000 + x = -7.031674368 + 6.666666665 x = -7.031674368 + 6.666666665 Combine like terms: -7.031674368 + 6.666666665 = -0.365007703 x = -0.365007703 Simplifying x = -0.365007703Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.698341033, -0.365007703}
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