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Simplifying 110x + -1(2500 + 10x + 0.2x2) = 0 110x + (2500 * -1 + 10x * -1 + 0.2x2 * -1) = 0 110x + (-2500 + -10x + -0.2x2) = 0 Reorder the terms: -2500 + 110x + -10x + -0.2x2 = 0 Combine like terms: 110x + -10x = 100x -2500 + 100x + -0.2x2 = 0 Solving -2500 + 100x + -0.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.2 the coefficient of the squared term: Divide each side by '-0.2'. 12500 + -500x + x2 = 0 Move the constant term to the right: Add '-12500' to each side of the equation. 12500 + -500x + -12500 + x2 = 0 + -12500 Reorder the terms: 12500 + -12500 + -500x + x2 = 0 + -12500 Combine like terms: 12500 + -12500 = 0 0 + -500x + x2 = 0 + -12500 -500x + x2 = 0 + -12500 Combine like terms: 0 + -12500 = -12500 -500x + x2 = -12500 The x term is -500x. Take half its coefficient (-250). Square it (62500) and add it to both sides. Add '62500' to each side of the equation. -500x + 62500 + x2 = -12500 + 62500 Reorder the terms: 62500 + -500x + x2 = -12500 + 62500 Combine like terms: -12500 + 62500 = 50000 62500 + -500x + x2 = 50000 Factor a perfect square on the left side: (x + -250)(x + -250) = 50000 Calculate the square root of the right side: 223.60679775 Break this problem into two subproblems by setting (x + -250) equal to 223.60679775 and -223.60679775.Subproblem 1
x + -250 = 223.60679775 Simplifying x + -250 = 223.60679775 Reorder the terms: -250 + x = 223.60679775 Solving -250 + x = 223.60679775 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '250' to each side of the equation. -250 + 250 + x = 223.60679775 + 250 Combine like terms: -250 + 250 = 0 0 + x = 223.60679775 + 250 x = 223.60679775 + 250 Combine like terms: 223.60679775 + 250 = 473.60679775 x = 473.60679775 Simplifying x = 473.60679775Subproblem 2
x + -250 = -223.60679775 Simplifying x + -250 = -223.60679775 Reorder the terms: -250 + x = -223.60679775 Solving -250 + x = -223.60679775 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '250' to each side of the equation. -250 + 250 + x = -223.60679775 + 250 Combine like terms: -250 + 250 = 0 0 + x = -223.60679775 + 250 x = -223.60679775 + 250 Combine like terms: -223.60679775 + 250 = 26.39320225 x = 26.39320225 Simplifying x = 26.39320225Solution
The solution to the problem is based on the solutions from the subproblems. x = {473.60679775, 26.39320225}
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