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Simplifying -241 = -4.9x2 + 85x Reorder the terms: -241 = 85x + -4.9x2 Solving -241 = 85x + -4.9x2 Solving for variable 'x'. Reorder the terms: -241 + -85x + 4.9x2 = 85x + -85x + -4.9x2 + 4.9x2 Combine like terms: 85x + -85x = 0 -241 + -85x + 4.9x2 = 0 + -4.9x2 + 4.9x2 -241 + -85x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -241 + -85x + 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'. -49.18367347 + -17.34693878x + x2 = 0 Move the constant term to the right: Add '49.18367347' to each side of the equation. -49.18367347 + -17.34693878x + 49.18367347 + x2 = 0 + 49.18367347 Reorder the terms: -49.18367347 + 49.18367347 + -17.34693878x + x2 = 0 + 49.18367347 Combine like terms: -49.18367347 + 49.18367347 = 0.00000000 0.00000000 + -17.34693878x + x2 = 0 + 49.18367347 -17.34693878x + x2 = 0 + 49.18367347 Combine like terms: 0 + 49.18367347 = 49.18367347 -17.34693878x + x2 = 49.18367347 The x term is -17.34693878x. Take half its coefficient (-8.67346939). Square it (75.22907126) and add it to both sides. Add '75.22907126' to each side of the equation. -17.34693878x + 75.22907126 + x2 = 49.18367347 + 75.22907126 Reorder the terms: 75.22907126 + -17.34693878x + x2 = 49.18367347 + 75.22907126 Combine like terms: 49.18367347 + 75.22907126 = 124.41274473 75.22907126 + -17.34693878x + x2 = 124.41274473 Factor a perfect square on the left side: (x + -8.67346939)(x + -8.67346939) = 124.41274473 Calculate the square root of the right side: 11.154046115 Break this problem into two subproblems by setting (x + -8.67346939) equal to 11.154046115 and -11.154046115.Subproblem 1
x + -8.67346939 = 11.154046115 Simplifying x + -8.67346939 = 11.154046115 Reorder the terms: -8.67346939 + x = 11.154046115 Solving -8.67346939 + x = 11.154046115 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.67346939' to each side of the equation. -8.67346939 + 8.67346939 + x = 11.154046115 + 8.67346939 Combine like terms: -8.67346939 + 8.67346939 = 0.00000000 0.00000000 + x = 11.154046115 + 8.67346939 x = 11.154046115 + 8.67346939 Combine like terms: 11.154046115 + 8.67346939 = 19.827515505 x = 19.827515505 Simplifying x = 19.827515505Subproblem 2
x + -8.67346939 = -11.154046115 Simplifying x + -8.67346939 = -11.154046115 Reorder the terms: -8.67346939 + x = -11.154046115 Solving -8.67346939 + x = -11.154046115 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.67346939' to each side of the equation. -8.67346939 + 8.67346939 + x = -11.154046115 + 8.67346939 Combine like terms: -8.67346939 + 8.67346939 = 0.00000000 0.00000000 + x = -11.154046115 + 8.67346939 x = -11.154046115 + 8.67346939 Combine like terms: -11.154046115 + 8.67346939 = -2.480576725 x = -2.480576725 Simplifying x = -2.480576725Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.827515505, -2.480576725}
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