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Simplifying x2 + 200x = -16 Reorder the terms: 200x + x2 = -16 Solving 200x + x2 = -16 Solving for variable 'x'. Reorder the terms: 16 + 200x + x2 = -16 + 16 Combine like terms: -16 + 16 = 0 16 + 200x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + 200x + -16 + x2 = 0 + -16 Reorder the terms: 16 + -16 + 200x + x2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + 200x + x2 = 0 + -16 200x + x2 = 0 + -16 Combine like terms: 0 + -16 = -16 200x + x2 = -16 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 = -16 + 10000 Reorder the terms: 10000 + 200x + x2 = -16 + 10000 Combine like terms: -16 + 10000 = 9984 10000 + 200x + x2 = 9984 Factor a perfect square on the left side: (x + 100)(x + 100) = 9984 Calculate the square root of the right side: 99.919967974 Break this problem into two subproblems by setting (x + 100) equal to 99.919967974 and -99.919967974.Subproblem 1
x + 100 = 99.919967974 Simplifying x + 100 = 99.919967974 Reorder the terms: 100 + x = 99.919967974 Solving 100 + x = 99.919967974 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 = 99.919967974 + -100 Combine like terms: 100 + -100 = 0 0 + x = 99.919967974 + -100 x = 99.919967974 + -100 Combine like terms: 99.919967974 + -100 = -0.080032026 x = -0.080032026 Simplifying x = -0.080032026Subproblem 2
x + 100 = -99.919967974 Simplifying x + 100 = -99.919967974 Reorder the terms: 100 + x = -99.919967974 Solving 100 + x = -99.919967974 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 = -99.919967974 + -100 Combine like terms: 100 + -100 = 0 0 + x = -99.919967974 + -100 x = -99.919967974 + -100 Combine like terms: -99.919967974 + -100 = -199.919967974 x = -199.919967974 Simplifying x = -199.919967974Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.080032026, -199.919967974}
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