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Simplifying -0.01x2 + 26x + 16500 = 0 Reorder the terms: 16500 + 26x + -0.01x2 = 0 Solving 16500 + 26x + -0.01x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.01 the coefficient of the squared term: Divide each side by '-0.01'. -1650000 + -2600x + x2 = 0 Move the constant term to the right: Add '1650000' to each side of the equation. -1650000 + -2600x + 1650000 + x2 = 0 + 1650000 Reorder the terms: -1650000 + 1650000 + -2600x + x2 = 0 + 1650000 Combine like terms: -1650000 + 1650000 = 0 0 + -2600x + x2 = 0 + 1650000 -2600x + x2 = 0 + 1650000 Combine like terms: 0 + 1650000 = 1650000 -2600x + x2 = 1650000 The x term is -2600x. Take half its coefficient (-1300). Square it (1690000) and add it to both sides. Add '1690000' to each side of the equation. -2600x + 1690000 + x2 = 1650000 + 1690000 Reorder the terms: 1690000 + -2600x + x2 = 1650000 + 1690000 Combine like terms: 1650000 + 1690000 = 3340000 1690000 + -2600x + x2 = 3340000 Factor a perfect square on the left side: (x + -1300)(x + -1300) = 3340000 Calculate the square root of the right side: 1827.56668825 Break this problem into two subproblems by setting (x + -1300) equal to 1827.56668825 and -1827.56668825.Subproblem 1
x + -1300 = 1827.56668825 Simplifying x + -1300 = 1827.56668825 Reorder the terms: -1300 + x = 1827.56668825 Solving -1300 + x = 1827.56668825 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1300' to each side of the equation. -1300 + 1300 + x = 1827.56668825 + 1300 Combine like terms: -1300 + 1300 = 0 0 + x = 1827.56668825 + 1300 x = 1827.56668825 + 1300 Combine like terms: 1827.56668825 + 1300 = 3127.56668825 x = 3127.56668825 Simplifying x = 3127.56668825Subproblem 2
x + -1300 = -1827.56668825 Simplifying x + -1300 = -1827.56668825 Reorder the terms: -1300 + x = -1827.56668825 Solving -1300 + x = -1827.56668825 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1300' to each side of the equation. -1300 + 1300 + x = -1827.56668825 + 1300 Combine like terms: -1300 + 1300 = 0 0 + x = -1827.56668825 + 1300 x = -1827.56668825 + 1300 Combine like terms: -1827.56668825 + 1300 = -527.56668825 x = -527.56668825 Simplifying x = -527.56668825Solution
The solution to the problem is based on the solutions from the subproblems. x = {3127.56668825, -527.56668825}
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