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Simplifying -0.1x2 + 18x + -200 = 0 Reorder the terms: -200 + 18x + -0.1x2 = 0 Solving -200 + 18x + -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 + -180x + x2 = 0 Move the constant term to the right: Add '-2000' to each side of the equation. 2000 + -180x + -2000 + x2 = 0 + -2000 Reorder the terms: 2000 + -2000 + -180x + x2 = 0 + -2000 Combine like terms: 2000 + -2000 = 0 0 + -180x + x2 = 0 + -2000 -180x + x2 = 0 + -2000 Combine like terms: 0 + -2000 = -2000 -180x + x2 = -2000 The x term is -180x. Take half its coefficient (-90). Square it (8100) and add it to both sides. Add '8100' to each side of the equation. -180x + 8100 + x2 = -2000 + 8100 Reorder the terms: 8100 + -180x + x2 = -2000 + 8100 Combine like terms: -2000 + 8100 = 6100 8100 + -180x + x2 = 6100 Factor a perfect square on the left side: (x + -90)(x + -90) = 6100 Calculate the square root of the right side: 78.102496759 Break this problem into two subproblems by setting (x + -90) equal to 78.102496759 and -78.102496759.Subproblem 1
x + -90 = 78.102496759 Simplifying x + -90 = 78.102496759 Reorder the terms: -90 + x = 78.102496759 Solving -90 + x = 78.102496759 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '90' to each side of the equation. -90 + 90 + x = 78.102496759 + 90 Combine like terms: -90 + 90 = 0 0 + x = 78.102496759 + 90 x = 78.102496759 + 90 Combine like terms: 78.102496759 + 90 = 168.102496759 x = 168.102496759 Simplifying x = 168.102496759Subproblem 2
x + -90 = -78.102496759 Simplifying x + -90 = -78.102496759 Reorder the terms: -90 + x = -78.102496759 Solving -90 + x = -78.102496759 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '90' to each side of the equation. -90 + 90 + x = -78.102496759 + 90 Combine like terms: -90 + 90 = 0 0 + x = -78.102496759 + 90 x = -78.102496759 + 90 Combine like terms: -78.102496759 + 90 = 11.897503241 x = 11.897503241 Simplifying x = 11.897503241Solution
The solution to the problem is based on the solutions from the subproblems. x = {168.102496759, 11.897503241}
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