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Simplifying -0.2x2 + 39x = 170 Reorder the terms: 39x + -0.2x2 = 170 Solving 39x + -0.2x2 = 170 Solving for variable 'x'. Reorder the terms: -170 + 39x + -0.2x2 = 170 + -170 Combine like terms: 170 + -170 = 0 -170 + 39x + -0.2x2 = 0 Begin completing the square. Divide all terms by -0.2 the coefficient of the squared term: Divide each side by '-0.2'. 850 + -195x + x2 = 0 Move the constant term to the right: Add '-850' to each side of the equation. 850 + -195x + -850 + x2 = 0 + -850 Reorder the terms: 850 + -850 + -195x + x2 = 0 + -850 Combine like terms: 850 + -850 = 0 0 + -195x + x2 = 0 + -850 -195x + x2 = 0 + -850 Combine like terms: 0 + -850 = -850 -195x + x2 = -850 The x term is -195x. Take half its coefficient (-97.5). Square it (9506.25) and add it to both sides. Add '9506.25' to each side of the equation. -195x + 9506.25 + x2 = -850 + 9506.25 Reorder the terms: 9506.25 + -195x + x2 = -850 + 9506.25 Combine like terms: -850 + 9506.25 = 8656.25 9506.25 + -195x + x2 = 8656.25 Factor a perfect square on the left side: (x + -97.5)(x + -97.5) = 8656.25 Calculate the square root of the right side: 93.03897033 Break this problem into two subproblems by setting (x + -97.5) equal to 93.03897033 and -93.03897033.Subproblem 1
x + -97.5 = 93.03897033 Simplifying x + -97.5 = 93.03897033 Reorder the terms: -97.5 + x = 93.03897033 Solving -97.5 + x = 93.03897033 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '97.5' to each side of the equation. -97.5 + 97.5 + x = 93.03897033 + 97.5 Combine like terms: -97.5 + 97.5 = 0.0 0.0 + x = 93.03897033 + 97.5 x = 93.03897033 + 97.5 Combine like terms: 93.03897033 + 97.5 = 190.53897033 x = 190.53897033 Simplifying x = 190.53897033Subproblem 2
x + -97.5 = -93.03897033 Simplifying x + -97.5 = -93.03897033 Reorder the terms: -97.5 + x = -93.03897033 Solving -97.5 + x = -93.03897033 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '97.5' to each side of the equation. -97.5 + 97.5 + x = -93.03897033 + 97.5 Combine like terms: -97.5 + 97.5 = 0.0 0.0 + x = -93.03897033 + 97.5 x = -93.03897033 + 97.5 Combine like terms: -93.03897033 + 97.5 = 4.46102967 x = 4.46102967 Simplifying x = 4.46102967Solution
The solution to the problem is based on the solutions from the subproblems. x = {190.53897033, 4.46102967}
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