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Simplifying x2 + 5000x + -3400 = 0 Reorder the terms: -3400 + 5000x + x2 = 0 Solving -3400 + 5000x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3400' to each side of the equation. -3400 + 5000x + 3400 + x2 = 0 + 3400 Reorder the terms: -3400 + 3400 + 5000x + x2 = 0 + 3400 Combine like terms: -3400 + 3400 = 0 0 + 5000x + x2 = 0 + 3400 5000x + x2 = 0 + 3400 Combine like terms: 0 + 3400 = 3400 5000x + x2 = 3400 The x term is 5000x. Take half its coefficient (2500). Square it (6250000) and add it to both sides. Add '6250000' to each side of the equation. 5000x + 6250000 + x2 = 3400 + 6250000 Reorder the terms: 6250000 + 5000x + x2 = 3400 + 6250000 Combine like terms: 3400 + 6250000 = 6253400 6250000 + 5000x + x2 = 6253400 Factor a perfect square on the left side: (x + 2500)(x + 2500) = 6253400 Calculate the square root of the right side: 2500.679907545 Break this problem into two subproblems by setting (x + 2500) equal to 2500.679907545 and -2500.679907545.Subproblem 1
x + 2500 = 2500.679907545 Simplifying x + 2500 = 2500.679907545 Reorder the terms: 2500 + x = 2500.679907545 Solving 2500 + x = 2500.679907545 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2500' to each side of the equation. 2500 + -2500 + x = 2500.679907545 + -2500 Combine like terms: 2500 + -2500 = 0 0 + x = 2500.679907545 + -2500 x = 2500.679907545 + -2500 Combine like terms: 2500.679907545 + -2500 = 0.679907545 x = 0.679907545 Simplifying x = 0.679907545Subproblem 2
x + 2500 = -2500.679907545 Simplifying x + 2500 = -2500.679907545 Reorder the terms: 2500 + x = -2500.679907545 Solving 2500 + x = -2500.679907545 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2500' to each side of the equation. 2500 + -2500 + x = -2500.679907545 + -2500 Combine like terms: 2500 + -2500 = 0 0 + x = -2500.679907545 + -2500 x = -2500.679907545 + -2500 Combine like terms: -2500.679907545 + -2500 = -5000.679907545 x = -5000.679907545 Simplifying x = -5000.679907545Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.679907545, -5000.679907545}
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