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Simplifying 130x + -1(3250 + 9x + 0.1x2) = 0 130x + (3250 * -1 + 9x * -1 + 0.1x2 * -1) = 0 130x + (-3250 + -9x + -0.1x2) = 0 Reorder the terms: -3250 + 130x + -9x + -0.1x2 = 0 Combine like terms: 130x + -9x = 121x -3250 + 121x + -0.1x2 = 0 Solving -3250 + 121x + -0.1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.1 the coefficient of the squared term: Divide each side by '-0.1'. 32500 + -1210x + x2 = 0 Move the constant term to the right: Add '-32500' to each side of the equation. 32500 + -1210x + -32500 + x2 = 0 + -32500 Reorder the terms: 32500 + -32500 + -1210x + x2 = 0 + -32500 Combine like terms: 32500 + -32500 = 0 0 + -1210x + x2 = 0 + -32500 -1210x + x2 = 0 + -32500 Combine like terms: 0 + -32500 = -32500 -1210x + x2 = -32500 The x term is -1210x. Take half its coefficient (-605). Square it (366025) and add it to both sides. Add '366025' to each side of the equation. -1210x + 366025 + x2 = -32500 + 366025 Reorder the terms: 366025 + -1210x + x2 = -32500 + 366025 Combine like terms: -32500 + 366025 = 333525 366025 + -1210x + x2 = 333525 Factor a perfect square on the left side: (x + -605)(x + -605) = 333525 Calculate the square root of the right side: 577.516233538 Break this problem into two subproblems by setting (x + -605) equal to 577.516233538 and -577.516233538.Subproblem 1
x + -605 = 577.516233538 Simplifying x + -605 = 577.516233538 Reorder the terms: -605 + x = 577.516233538 Solving -605 + x = 577.516233538 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '605' to each side of the equation. -605 + 605 + x = 577.516233538 + 605 Combine like terms: -605 + 605 = 0 0 + x = 577.516233538 + 605 x = 577.516233538 + 605 Combine like terms: 577.516233538 + 605 = 1182.516233538 x = 1182.516233538 Simplifying x = 1182.516233538Subproblem 2
x + -605 = -577.516233538 Simplifying x + -605 = -577.516233538 Reorder the terms: -605 + x = -577.516233538 Solving -605 + x = -577.516233538 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '605' to each side of the equation. -605 + 605 + x = -577.516233538 + 605 Combine like terms: -605 + 605 = 0 0 + x = -577.516233538 + 605 x = -577.516233538 + 605 Combine like terms: -577.516233538 + 605 = 27.483766462 x = 27.483766462 Simplifying x = 27.483766462Solution
The solution to the problem is based on the solutions from the subproblems. x = {1182.516233538, 27.483766462}
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