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Simplifying 2x2 + 5x = 200 Reorder the terms: 5x + 2x2 = 200 Solving 5x + 2x2 = 200 Solving for variable 'x'. Reorder the terms: -200 + 5x + 2x2 = 200 + -200 Combine like terms: 200 + -200 = 0 -200 + 5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -100 + 2.5x + x2 = 0 Move the constant term to the right: Add '100' to each side of the equation. -100 + 2.5x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + 2.5x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 2.5x + x2 = 0 + 100 2.5x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 2.5x + x2 = 100 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 100 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 100 + 1.5625 Combine like terms: 100 + 1.5625 = 101.5625 1.5625 + 2.5x + x2 = 101.5625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 101.5625 Calculate the square root of the right side: 10.077822185 Break this problem into two subproblems by setting (x + 1.25) equal to 10.077822185 and -10.077822185.Subproblem 1
x + 1.25 = 10.077822185 Simplifying x + 1.25 = 10.077822185 Reorder the terms: 1.25 + x = 10.077822185 Solving 1.25 + x = 10.077822185 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 10.077822185 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 10.077822185 + -1.25 x = 10.077822185 + -1.25 Combine like terms: 10.077822185 + -1.25 = 8.827822185 x = 8.827822185 Simplifying x = 8.827822185Subproblem 2
x + 1.25 = -10.077822185 Simplifying x + 1.25 = -10.077822185 Reorder the terms: 1.25 + x = -10.077822185 Solving 1.25 + x = -10.077822185 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -10.077822185 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -10.077822185 + -1.25 x = -10.077822185 + -1.25 Combine like terms: -10.077822185 + -1.25 = -11.327822185 x = -11.327822185 Simplifying x = -11.327822185Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.827822185, -11.327822185}
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