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Simplifying -0.01x2 + 130x + -180000 = 174900 Reorder the terms: -180000 + 130x + -0.01x2 = 174900 Solving -180000 + 130x + -0.01x2 = 174900 Solving for variable 'x'. Reorder the terms: -180000 + -174900 + 130x + -0.01x2 = 174900 + -174900 Combine like terms: -180000 + -174900 = -354900 -354900 + 130x + -0.01x2 = 174900 + -174900 Combine like terms: 174900 + -174900 = 0 -354900 + 130x + -0.01x2 = 0 Begin completing the square. Divide all terms by -0.01 the coefficient of the squared term: Divide each side by '-0.01'. 35490000 + -13000x + x2 = 0 Move the constant term to the right: Add '-35490000' to each side of the equation. 35490000 + -13000x + -35490000 + x2 = 0 + -35490000 Reorder the terms: 35490000 + -35490000 + -13000x + x2 = 0 + -35490000 Combine like terms: 35490000 + -35490000 = 0 0 + -13000x + x2 = 0 + -35490000 -13000x + x2 = 0 + -35490000 Combine like terms: 0 + -35490000 = -35490000 -13000x + x2 = -35490000 The x term is -13000x. Take half its coefficient (-6500). Square it (42250000) and add it to both sides. Add '42250000' to each side of the equation. -13000x + 42250000 + x2 = -35490000 + 42250000 Reorder the terms: 42250000 + -13000x + x2 = -35490000 + 42250000 Combine like terms: -35490000 + 42250000 = 6760000 42250000 + -13000x + x2 = 6760000 Factor a perfect square on the left side: (x + -6500)(x + -6500) = 6760000 Calculate the square root of the right side: 2600 Break this problem into two subproblems by setting (x + -6500) equal to 2600 and -2600.Subproblem 1
x + -6500 = 2600 Simplifying x + -6500 = 2600 Reorder the terms: -6500 + x = 2600 Solving -6500 + x = 2600 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6500' to each side of the equation. -6500 + 6500 + x = 2600 + 6500 Combine like terms: -6500 + 6500 = 0 0 + x = 2600 + 6500 x = 2600 + 6500 Combine like terms: 2600 + 6500 = 9100 x = 9100 Simplifying x = 9100Subproblem 2
x + -6500 = -2600 Simplifying x + -6500 = -2600 Reorder the terms: -6500 + x = -2600 Solving -6500 + x = -2600 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6500' to each side of the equation. -6500 + 6500 + x = -2600 + 6500 Combine like terms: -6500 + 6500 = 0 0 + x = -2600 + 6500 x = -2600 + 6500 Combine like terms: -2600 + 6500 = 3900 x = 3900 Simplifying x = 3900Solution
The solution to the problem is based on the solutions from the subproblems. x = {9100, 3900}
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