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Simplifying 0 = 60 + 12.5x + -4.9x2 Solving 0 = 60 + 12.5x + -4.9x2 Solving for variable 'x'. Combine like terms: 0 + -60 = -60 -60 + -12.5x + 4.9x2 = 60 + 12.5x + -4.9x2 + -60 + -12.5x + 4.9x2 Reorder the terms: -60 + -12.5x + 4.9x2 = 60 + -60 + 12.5x + -12.5x + -4.9x2 + 4.9x2 Combine like terms: 60 + -60 = 0 -60 + -12.5x + 4.9x2 = 0 + 12.5x + -12.5x + -4.9x2 + 4.9x2 -60 + -12.5x + 4.9x2 = 12.5x + -12.5x + -4.9x2 + 4.9x2 Combine like terms: 12.5x + -12.5x = 0.0 -60 + -12.5x + 4.9x2 = 0.0 + -4.9x2 + 4.9x2 -60 + -12.5x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -60 + -12.5x + 4.9x2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -12.24489796 + -2.551020408x + x2 = 0 Move the constant term to the right: Add '12.24489796' to each side of the equation. -12.24489796 + -2.551020408x + 12.24489796 + x2 = 0 + 12.24489796 Reorder the terms: -12.24489796 + 12.24489796 + -2.551020408x + x2 = 0 + 12.24489796 Combine like terms: -12.24489796 + 12.24489796 = 0.00000000 0.00000000 + -2.551020408x + x2 = 0 + 12.24489796 -2.551020408x + x2 = 0 + 12.24489796 Combine like terms: 0 + 12.24489796 = 12.24489796 -2.551020408x + x2 = 12.24489796 The x term is -2.551020408x. Take half its coefficient (-1.275510204). Square it (1.626926281) and add it to both sides. Add '1.626926281' to each side of the equation. -2.551020408x + 1.626926281 + x2 = 12.24489796 + 1.626926281 Reorder the terms: 1.626926281 + -2.551020408x + x2 = 12.24489796 + 1.626926281 Combine like terms: 12.24489796 + 1.626926281 = 13.871824241 1.626926281 + -2.551020408x + x2 = 13.871824241 Factor a perfect square on the left side: (x + -1.275510204)(x + -1.275510204) = 13.871824241 Calculate the square root of the right side: 3.724489796 Break this problem into two subproblems by setting (x + -1.275510204) equal to 3.724489796 and -3.724489796.Subproblem 1
x + -1.275510204 = 3.724489796 Simplifying x + -1.275510204 = 3.724489796 Reorder the terms: -1.275510204 + x = 3.724489796 Solving -1.275510204 + x = 3.724489796 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.275510204' to each side of the equation. -1.275510204 + 1.275510204 + x = 3.724489796 + 1.275510204 Combine like terms: -1.275510204 + 1.275510204 = 0.000000000 0.000000000 + x = 3.724489796 + 1.275510204 x = 3.724489796 + 1.275510204 Combine like terms: 3.724489796 + 1.275510204 = 5 x = 5 Simplifying x = 5Subproblem 2
x + -1.275510204 = -3.724489796 Simplifying x + -1.275510204 = -3.724489796 Reorder the terms: -1.275510204 + x = -3.724489796 Solving -1.275510204 + x = -3.724489796 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.275510204' to each side of the equation. -1.275510204 + 1.275510204 + x = -3.724489796 + 1.275510204 Combine like terms: -1.275510204 + 1.275510204 = 0.000000000 0.000000000 + x = -3.724489796 + 1.275510204 x = -3.724489796 + 1.275510204 Combine like terms: -3.724489796 + 1.275510204 = -2.448979592 x = -2.448979592 Simplifying x = -2.448979592Solution
The solution to the problem is based on the solutions from the subproblems. x = {5, -2.448979592}
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