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Simplifying x = 20(-5x2 + 200) Reorder the terms: x = 20(200 + -5x2) x = (200 * 20 + -5x2 * 20) x = (4000 + -100x2) Solving x = 4000 + -100x2 Solving for variable 'x'. Reorder the terms: -4000 + x + 100x2 = 4000 + -100x2 + -4000 + 100x2 Reorder the terms: -4000 + x + 100x2 = 4000 + -4000 + -100x2 + 100x2 Combine like terms: 4000 + -4000 = 0 -4000 + x + 100x2 = 0 + -100x2 + 100x2 -4000 + x + 100x2 = -100x2 + 100x2 Combine like terms: -100x2 + 100x2 = 0 -4000 + x + 100x2 = 0 Begin completing the square. Divide all terms by 100 the coefficient of the squared term: Divide each side by '100'. -40 + 0.01x + x2 = 0 Move the constant term to the right: Add '40' to each side of the equation. -40 + 0.01x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + 0.01x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + 0.01x + x2 = 0 + 40 0.01x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 0.01x + x2 = 40 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.01x + 0.25 + x2 = 40 + 0.25 Reorder the terms: 0.25 + 0.01x + x2 = 40 + 0.25 Combine like terms: 40 + 0.25 = 40.25 0.25 + 0.01x + x2 = 40.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 40.25 Calculate the square root of the right side: 6.34428877 Break this problem into two subproblems by setting (x + 0.5) equal to 6.34428877 and -6.34428877.Subproblem 1
x + 0.5 = 6.34428877 Simplifying x + 0.5 = 6.34428877 Reorder the terms: 0.5 + x = 6.34428877 Solving 0.5 + x = 6.34428877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 6.34428877 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 6.34428877 + -0.5 x = 6.34428877 + -0.5 Combine like terms: 6.34428877 + -0.5 = 5.84428877 x = 5.84428877 Simplifying x = 5.84428877Subproblem 2
x + 0.5 = -6.34428877 Simplifying x + 0.5 = -6.34428877 Reorder the terms: 0.5 + x = -6.34428877 Solving 0.5 + x = -6.34428877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -6.34428877 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -6.34428877 + -0.5 x = -6.34428877 + -0.5 Combine like terms: -6.34428877 + -0.5 = -6.84428877 x = -6.84428877 Simplifying x = -6.84428877Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.84428877, -6.84428877}
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