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Simplifying -0.01x2 + 13x + -1700 = 0 Reorder the terms: -1700 + 13x + -0.01x2 = 0 Solving -1700 + 13x + -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'. 170000 + -1300x + x2 = 0 Move the constant term to the right: Add '-170000' to each side of the equation. 170000 + -1300x + -170000 + x2 = 0 + -170000 Reorder the terms: 170000 + -170000 + -1300x + x2 = 0 + -170000 Combine like terms: 170000 + -170000 = 0 0 + -1300x + x2 = 0 + -170000 -1300x + x2 = 0 + -170000 Combine like terms: 0 + -170000 = -170000 -1300x + x2 = -170000 The x term is -1300x. Take half its coefficient (-650). Square it (422500) and add it to both sides. Add '422500' to each side of the equation. -1300x + 422500 + x2 = -170000 + 422500 Reorder the terms: 422500 + -1300x + x2 = -170000 + 422500 Combine like terms: -170000 + 422500 = 252500 422500 + -1300x + x2 = 252500 Factor a perfect square on the left side: (x + -650)(x + -650) = 252500 Calculate the square root of the right side: 502.493781056 Break this problem into two subproblems by setting (x + -650) equal to 502.493781056 and -502.493781056.Subproblem 1
x + -650 = 502.493781056 Simplifying x + -650 = 502.493781056 Reorder the terms: -650 + x = 502.493781056 Solving -650 + x = 502.493781056 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '650' to each side of the equation. -650 + 650 + x = 502.493781056 + 650 Combine like terms: -650 + 650 = 0 0 + x = 502.493781056 + 650 x = 502.493781056 + 650 Combine like terms: 502.493781056 + 650 = 1152.493781056 x = 1152.493781056 Simplifying x = 1152.493781056Subproblem 2
x + -650 = -502.493781056 Simplifying x + -650 = -502.493781056 Reorder the terms: -650 + x = -502.493781056 Solving -650 + x = -502.493781056 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '650' to each side of the equation. -650 + 650 + x = -502.493781056 + 650 Combine like terms: -650 + 650 = 0 0 + x = -502.493781056 + 650 x = -502.493781056 + 650 Combine like terms: -502.493781056 + 650 = 147.506218944 x = 147.506218944 Simplifying x = 147.506218944Solution
The solution to the problem is based on the solutions from the subproblems. x = {1152.493781056, 147.506218944}
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