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Simplifying x2 + 200x + -15200 = 0 Reorder the terms: -15200 + 200x + x2 = 0 Solving -15200 + 200x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '15200' to each side of the equation. -15200 + 200x + 15200 + x2 = 0 + 15200 Reorder the terms: -15200 + 15200 + 200x + x2 = 0 + 15200 Combine like terms: -15200 + 15200 = 0 0 + 200x + x2 = 0 + 15200 200x + x2 = 0 + 15200 Combine like terms: 0 + 15200 = 15200 200x + x2 = 15200 The x term is 200x. Take half its coefficient (100). Square it (10000) and add it to both sides. Add '10000' to each side of the equation. 200x + 10000 + x2 = 15200 + 10000 Reorder the terms: 10000 + 200x + x2 = 15200 + 10000 Combine like terms: 15200 + 10000 = 25200 10000 + 200x + x2 = 25200 Factor a perfect square on the left side: (x + 100)(x + 100) = 25200 Calculate the square root of the right side: 158.745078664 Break this problem into two subproblems by setting (x + 100) equal to 158.745078664 and -158.745078664.Subproblem 1
x + 100 = 158.745078664 Simplifying x + 100 = 158.745078664 Reorder the terms: 100 + x = 158.745078664 Solving 100 + x = 158.745078664 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-100' to each side of the equation. 100 + -100 + x = 158.745078664 + -100 Combine like terms: 100 + -100 = 0 0 + x = 158.745078664 + -100 x = 158.745078664 + -100 Combine like terms: 158.745078664 + -100 = 58.745078664 x = 58.745078664 Simplifying x = 58.745078664Subproblem 2
x + 100 = -158.745078664 Simplifying x + 100 = -158.745078664 Reorder the terms: 100 + x = -158.745078664 Solving 100 + x = -158.745078664 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-100' to each side of the equation. 100 + -100 + x = -158.745078664 + -100 Combine like terms: 100 + -100 = 0 0 + x = -158.745078664 + -100 x = -158.745078664 + -100 Combine like terms: -158.745078664 + -100 = -258.745078664 x = -258.745078664 Simplifying x = -258.745078664Solution
The solution to the problem is based on the solutions from the subproblems. x = {58.745078664, -258.745078664}
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