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Simplifying 25 = 10x + -0.83x2 Solving 25 = 10x + -0.83x2 Solving for variable 'x'. Reorder the terms: 25 + -10x + 0.83x2 = 10x + -10x + -0.83x2 + 0.83x2 Combine like terms: 10x + -10x = 0 25 + -10x + 0.83x2 = 0 + -0.83x2 + 0.83x2 25 + -10x + 0.83x2 = -0.83x2 + 0.83x2 Combine like terms: -0.83x2 + 0.83x2 = 0.00 25 + -10x + 0.83x2 = 0.00 Begin completing the square. Divide all terms by 0.83 the coefficient of the squared term: Divide each side by '0.83'. 30.12048193 + -12.04819277x + x2 = 0 Move the constant term to the right: Add '-30.12048193' to each side of the equation. 30.12048193 + -12.04819277x + -30.12048193 + x2 = 0 + -30.12048193 Reorder the terms: 30.12048193 + -30.12048193 + -12.04819277x + x2 = 0 + -30.12048193 Combine like terms: 30.12048193 + -30.12048193 = 0.00000000 0.00000000 + -12.04819277x + x2 = 0 + -30.12048193 -12.04819277x + x2 = 0 + -30.12048193 Combine like terms: 0 + -30.12048193 = -30.12048193 -12.04819277x + x2 = -30.12048193 The x term is -12.04819277x. Take half its coefficient (-6.024096385). Square it (36.28973726) and add it to both sides. Add '36.28973726' to each side of the equation. -12.04819277x + 36.28973726 + x2 = -30.12048193 + 36.28973726 Reorder the terms: 36.28973726 + -12.04819277x + x2 = -30.12048193 + 36.28973726 Combine like terms: -30.12048193 + 36.28973726 = 6.16925533 36.28973726 + -12.04819277x + x2 = 6.16925533 Factor a perfect square on the left side: (x + -6.024096385)(x + -6.024096385) = 6.16925533 Calculate the square root of the right side: 2.483798569 Break this problem into two subproblems by setting (x + -6.024096385) equal to 2.483798569 and -2.483798569.Subproblem 1
x + -6.024096385 = 2.483798569 Simplifying x + -6.024096385 = 2.483798569 Reorder the terms: -6.024096385 + x = 2.483798569 Solving -6.024096385 + x = 2.483798569 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.024096385' to each side of the equation. -6.024096385 + 6.024096385 + x = 2.483798569 + 6.024096385 Combine like terms: -6.024096385 + 6.024096385 = 0.000000000 0.000000000 + x = 2.483798569 + 6.024096385 x = 2.483798569 + 6.024096385 Combine like terms: 2.483798569 + 6.024096385 = 8.507894954 x = 8.507894954 Simplifying x = 8.507894954Subproblem 2
x + -6.024096385 = -2.483798569 Simplifying x + -6.024096385 = -2.483798569 Reorder the terms: -6.024096385 + x = -2.483798569 Solving -6.024096385 + x = -2.483798569 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.024096385' to each side of the equation. -6.024096385 + 6.024096385 + x = -2.483798569 + 6.024096385 Combine like terms: -6.024096385 + 6.024096385 = 0.000000000 0.000000000 + x = -2.483798569 + 6.024096385 x = -2.483798569 + 6.024096385 Combine like terms: -2.483798569 + 6.024096385 = 3.540297816 x = 3.540297816 Simplifying x = 3.540297816Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.507894954, 3.540297816}
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