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Simplifying 0.025(x2) + -3x + -24910 = 0 Reorder the terms: -24910 + -3x + 0.025x2 = 0 Solving -24910 + -3x + 0.025x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.025 the coefficient of the squared term: Divide each side by '0.025'. -996400 + -120x + x2 = 0 Move the constant term to the right: Add '996400' to each side of the equation. -996400 + -120x + 996400 + x2 = 0 + 996400 Reorder the terms: -996400 + 996400 + -120x + x2 = 0 + 996400 Combine like terms: -996400 + 996400 = 0 0 + -120x + x2 = 0 + 996400 -120x + x2 = 0 + 996400 Combine like terms: 0 + 996400 = 996400 -120x + x2 = 996400 The x term is -120x. Take half its coefficient (-60). Square it (3600) and add it to both sides. Add '3600' to each side of the equation. -120x + 3600 + x2 = 996400 + 3600 Reorder the terms: 3600 + -120x + x2 = 996400 + 3600 Combine like terms: 996400 + 3600 = 1000000 3600 + -120x + x2 = 1000000 Factor a perfect square on the left side: (x + -60)(x + -60) = 1000000 Calculate the square root of the right side: 1000 Break this problem into two subproblems by setting (x + -60) equal to 1000 and -1000.Subproblem 1
x + -60 = 1000 Simplifying x + -60 = 1000 Reorder the terms: -60 + x = 1000 Solving -60 + x = 1000 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '60' to each side of the equation. -60 + 60 + x = 1000 + 60 Combine like terms: -60 + 60 = 0 0 + x = 1000 + 60 x = 1000 + 60 Combine like terms: 1000 + 60 = 1060 x = 1060 Simplifying x = 1060Subproblem 2
x + -60 = -1000 Simplifying x + -60 = -1000 Reorder the terms: -60 + x = -1000 Solving -60 + x = -1000 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '60' to each side of the equation. -60 + 60 + x = -1000 + 60 Combine like terms: -60 + 60 = 0 0 + x = -1000 + 60 x = -1000 + 60 Combine like terms: -1000 + 60 = -940 x = -940 Simplifying x = -940Solution
The solution to the problem is based on the solutions from the subproblems. x = {1060, -940}
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