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Simplifying 100x + -1x2 = 200 Solving 100x + -1x2 = 200 Solving for variable 'x'. Reorder the terms: -200 + 100x + -1x2 = 200 + -200 Combine like terms: 200 + -200 = 0 -200 + 100x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 200 + -100x + x2 = 0 Move the constant term to the right: Add '-200' to each side of the equation. 200 + -100x + -200 + x2 = 0 + -200 Reorder the terms: 200 + -200 + -100x + x2 = 0 + -200 Combine like terms: 200 + -200 = 0 0 + -100x + x2 = 0 + -200 -100x + x2 = 0 + -200 Combine like terms: 0 + -200 = -200 -100x + x2 = -200 The x term is -100x. Take half its coefficient (-50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. -100x + 2500 + x2 = -200 + 2500 Reorder the terms: 2500 + -100x + x2 = -200 + 2500 Combine like terms: -200 + 2500 = 2300 2500 + -100x + x2 = 2300 Factor a perfect square on the left side: (x + -50)(x + -50) = 2300 Calculate the square root of the right side: 47.958315233 Break this problem into two subproblems by setting (x + -50) equal to 47.958315233 and -47.958315233.Subproblem 1
x + -50 = 47.958315233 Simplifying x + -50 = 47.958315233 Reorder the terms: -50 + x = 47.958315233 Solving -50 + x = 47.958315233 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = 47.958315233 + 50 Combine like terms: -50 + 50 = 0 0 + x = 47.958315233 + 50 x = 47.958315233 + 50 Combine like terms: 47.958315233 + 50 = 97.958315233 x = 97.958315233 Simplifying x = 97.958315233Subproblem 2
x + -50 = -47.958315233 Simplifying x + -50 = -47.958315233 Reorder the terms: -50 + x = -47.958315233 Solving -50 + x = -47.958315233 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = -47.958315233 + 50 Combine like terms: -50 + 50 = 0 0 + x = -47.958315233 + 50 x = -47.958315233 + 50 Combine like terms: -47.958315233 + 50 = 2.041684767 x = 2.041684767 Simplifying x = 2.041684767Solution
The solution to the problem is based on the solutions from the subproblems. x = {97.958315233, 2.041684767}
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