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Simplifying 36 = -5x2 + 100x Reorder the terms: 36 = 100x + -5x2 Solving 36 = 100x + -5x2 Solving for variable 'x'. Reorder the terms: 36 + -100x + 5x2 = 100x + -100x + -5x2 + 5x2 Combine like terms: 100x + -100x = 0 36 + -100x + 5x2 = 0 + -5x2 + 5x2 36 + -100x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 36 + -100x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 7.2 + -20x + x2 = 0 Move the constant term to the right: Add '-7.2' to each side of the equation. 7.2 + -20x + -7.2 + x2 = 0 + -7.2 Reorder the terms: 7.2 + -7.2 + -20x + x2 = 0 + -7.2 Combine like terms: 7.2 + -7.2 = 0.0 0.0 + -20x + x2 = 0 + -7.2 -20x + x2 = 0 + -7.2 Combine like terms: 0 + -7.2 = -7.2 -20x + x2 = -7.2 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 = -7.2 + 100 Reorder the terms: 100 + -20x + x2 = -7.2 + 100 Combine like terms: -7.2 + 100 = 92.8 100 + -20x + x2 = 92.8 Factor a perfect square on the left side: (x + -10)(x + -10) = 92.8 Calculate the square root of the right side: 9.633275663 Break this problem into two subproblems by setting (x + -10) equal to 9.633275663 and -9.633275663.Subproblem 1
x + -10 = 9.633275663 Simplifying x + -10 = 9.633275663 Reorder the terms: -10 + x = 9.633275663 Solving -10 + x = 9.633275663 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 = 9.633275663 + 10 Combine like terms: -10 + 10 = 0 0 + x = 9.633275663 + 10 x = 9.633275663 + 10 Combine like terms: 9.633275663 + 10 = 19.633275663 x = 19.633275663 Simplifying x = 19.633275663Subproblem 2
x + -10 = -9.633275663 Simplifying x + -10 = -9.633275663 Reorder the terms: -10 + x = -9.633275663 Solving -10 + x = -9.633275663 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 = -9.633275663 + 10 Combine like terms: -10 + 10 = 0 0 + x = -9.633275663 + 10 x = -9.633275663 + 10 Combine like terms: -9.633275663 + 10 = 0.366724337 x = 0.366724337 Simplifying x = 0.366724337Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.633275663, 0.366724337}
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