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Simplifying -900 = 0.1x2 + -20x Reorder the terms: -900 = -20x + 0.1x2 Solving -900 = -20x + 0.1x2 Solving for variable 'x'. Reorder the terms: -900 + 20x + -0.1x2 = -20x + 20x + 0.1x2 + -0.1x2 Combine like terms: -20x + 20x = 0 -900 + 20x + -0.1x2 = 0 + 0.1x2 + -0.1x2 -900 + 20x + -0.1x2 = 0.1x2 + -0.1x2 Combine like terms: 0.1x2 + -0.1x2 = 0.0 -900 + 20x + -0.1x2 = 0.0 Begin completing the square. Divide all terms by -0.1 the coefficient of the squared term: Divide each side by '-0.1'. 9000 + -200x + x2 = 0 Move the constant term to the right: Add '-9000' to each side of the equation. 9000 + -200x + -9000 + x2 = 0 + -9000 Reorder the terms: 9000 + -9000 + -200x + x2 = 0 + -9000 Combine like terms: 9000 + -9000 = 0 0 + -200x + x2 = 0 + -9000 -200x + x2 = 0 + -9000 Combine like terms: 0 + -9000 = -9000 -200x + x2 = -9000 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 = -9000 + 10000 Reorder the terms: 10000 + -200x + x2 = -9000 + 10000 Combine like terms: -9000 + 10000 = 1000 10000 + -200x + x2 = 1000 Factor a perfect square on the left side: (x + -100)(x + -100) = 1000 Calculate the square root of the right side: 31.622776602 Break this problem into two subproblems by setting (x + -100) equal to 31.622776602 and -31.622776602.Subproblem 1
x + -100 = 31.622776602 Simplifying x + -100 = 31.622776602 Reorder the terms: -100 + x = 31.622776602 Solving -100 + x = 31.622776602 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 = 31.622776602 + 100 Combine like terms: -100 + 100 = 0 0 + x = 31.622776602 + 100 x = 31.622776602 + 100 Combine like terms: 31.622776602 + 100 = 131.622776602 x = 131.622776602 Simplifying x = 131.622776602Subproblem 2
x + -100 = -31.622776602 Simplifying x + -100 = -31.622776602 Reorder the terms: -100 + x = -31.622776602 Solving -100 + x = -31.622776602 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 = -31.622776602 + 100 Combine like terms: -100 + 100 = 0 0 + x = -31.622776602 + 100 x = -31.622776602 + 100 Combine like terms: -31.622776602 + 100 = 68.377223398 x = 68.377223398 Simplifying x = 68.377223398Solution
The solution to the problem is based on the solutions from the subproblems. x = {131.622776602, 68.377223398}
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