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Simplifying x2 + 200x + 8800 = 0 Reorder the terms: 8800 + 200x + x2 = 0 Solving 8800 + 200x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-8800' to each side of the equation. 8800 + 200x + -8800 + x2 = 0 + -8800 Reorder the terms: 8800 + -8800 + 200x + x2 = 0 + -8800 Combine like terms: 8800 + -8800 = 0 0 + 200x + x2 = 0 + -8800 200x + x2 = 0 + -8800 Combine like terms: 0 + -8800 = -8800 200x + x2 = -8800 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 = -8800 + 10000 Reorder the terms: 10000 + 200x + x2 = -8800 + 10000 Combine like terms: -8800 + 10000 = 1200 10000 + 200x + x2 = 1200 Factor a perfect square on the left side: (x + 100)(x + 100) = 1200 Calculate the square root of the right side: 34.641016151 Break this problem into two subproblems by setting (x + 100) equal to 34.641016151 and -34.641016151.Subproblem 1
x + 100 = 34.641016151 Simplifying x + 100 = 34.641016151 Reorder the terms: 100 + x = 34.641016151 Solving 100 + x = 34.641016151 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 = 34.641016151 + -100 Combine like terms: 100 + -100 = 0 0 + x = 34.641016151 + -100 x = 34.641016151 + -100 Combine like terms: 34.641016151 + -100 = -65.358983849 x = -65.358983849 Simplifying x = -65.358983849Subproblem 2
x + 100 = -34.641016151 Simplifying x + 100 = -34.641016151 Reorder the terms: 100 + x = -34.641016151 Solving 100 + x = -34.641016151 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 = -34.641016151 + -100 Combine like terms: 100 + -100 = 0 0 + x = -34.641016151 + -100 x = -34.641016151 + -100 Combine like terms: -34.641016151 + -100 = -134.641016151 x = -134.641016151 Simplifying x = -134.641016151Solution
The solution to the problem is based on the solutions from the subproblems. x = {-65.358983849, -134.641016151}
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