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Simplifying 0.1x2 + -10x + 200 = 0 Reorder the terms: 200 + -10x + 0.1x2 = 0 Solving 200 + -10x + 0.1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.1 the coefficient of the squared term: Divide each side by '0.1'. 2000 + -100x + x2 = 0 Move the constant term to the right: Add '-2000' to each side of the equation. 2000 + -100x + -2000 + x2 = 0 + -2000 Reorder the terms: 2000 + -2000 + -100x + x2 = 0 + -2000 Combine like terms: 2000 + -2000 = 0 0 + -100x + x2 = 0 + -2000 -100x + x2 = 0 + -2000 Combine like terms: 0 + -2000 = -2000 -100x + x2 = -2000 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 = -2000 + 2500 Reorder the terms: 2500 + -100x + x2 = -2000 + 2500 Combine like terms: -2000 + 2500 = 500 2500 + -100x + x2 = 500 Factor a perfect square on the left side: (x + -50)(x + -50) = 500 Calculate the square root of the right side: 22.360679775 Break this problem into two subproblems by setting (x + -50) equal to 22.360679775 and -22.360679775.Subproblem 1
x + -50 = 22.360679775 Simplifying x + -50 = 22.360679775 Reorder the terms: -50 + x = 22.360679775 Solving -50 + x = 22.360679775 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 = 22.360679775 + 50 Combine like terms: -50 + 50 = 0 0 + x = 22.360679775 + 50 x = 22.360679775 + 50 Combine like terms: 22.360679775 + 50 = 72.360679775 x = 72.360679775 Simplifying x = 72.360679775Subproblem 2
x + -50 = -22.360679775 Simplifying x + -50 = -22.360679775 Reorder the terms: -50 + x = -22.360679775 Solving -50 + x = -22.360679775 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 = -22.360679775 + 50 Combine like terms: -50 + 50 = 0 0 + x = -22.360679775 + 50 x = -22.360679775 + 50 Combine like terms: -22.360679775 + 50 = 27.639320225 x = 27.639320225 Simplifying x = 27.639320225Solution
The solution to the problem is based on the solutions from the subproblems. x = {72.360679775, 27.639320225}
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