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Simplifying -61.3333 = 6x + -0.833333x2 Solving -61.3333 = 6x + -0.833333x2 Solving for variable 'x'. Reorder the terms: -61.3333 + -6x + 0.833333x2 = 6x + -6x + -0.833333x2 + 0.833333x2 Combine like terms: 6x + -6x = 0 -61.3333 + -6x + 0.833333x2 = 0 + -0.833333x2 + 0.833333x2 -61.3333 + -6x + 0.833333x2 = -0.833333x2 + 0.833333x2 Combine like terms: -0.833333x2 + 0.833333x2 = 0.000000 -61.3333 + -6x + 0.833333x2 = 0.000000 Begin completing the square. Divide all terms by 0.833333 the coefficient of the squared term: Divide each side by '0.833333'. -73.59998944 + -7.20000288x + x2 = 0 Move the constant term to the right: Add '73.59998944' to each side of the equation. -73.59998944 + -7.20000288x + 73.59998944 + x2 = 0 + 73.59998944 Reorder the terms: -73.59998944 + 73.59998944 + -7.20000288x + x2 = 0 + 73.59998944 Combine like terms: -73.59998944 + 73.59998944 = 0.00000000 0.00000000 + -7.20000288x + x2 = 0 + 73.59998944 -7.20000288x + x2 = 0 + 73.59998944 Combine like terms: 0 + 73.59998944 = 73.59998944 -7.20000288x + x2 = 73.59998944 The x term is -7.20000288x. Take half its coefficient (-3.60000144). Square it (12.96001037) and add it to both sides. Add '12.96001037' to each side of the equation. -7.20000288x + 12.96001037 + x2 = 73.59998944 + 12.96001037 Reorder the terms: 12.96001037 + -7.20000288x + x2 = 73.59998944 + 12.96001037 Combine like terms: 73.59998944 + 12.96001037 = 86.55999981 12.96001037 + -7.20000288x + x2 = 86.55999981 Factor a perfect square on the left side: (x + -3.60000144)(x + -3.60000144) = 86.55999981 Calculate the square root of the right side: 9.303762669 Break this problem into two subproblems by setting (x + -3.60000144) equal to 9.303762669 and -9.303762669.Subproblem 1
x + -3.60000144 = 9.303762669 Simplifying x + -3.60000144 = 9.303762669 Reorder the terms: -3.60000144 + x = 9.303762669 Solving -3.60000144 + x = 9.303762669 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.60000144' to each side of the equation. -3.60000144 + 3.60000144 + x = 9.303762669 + 3.60000144 Combine like terms: -3.60000144 + 3.60000144 = 0.00000000 0.00000000 + x = 9.303762669 + 3.60000144 x = 9.303762669 + 3.60000144 Combine like terms: 9.303762669 + 3.60000144 = 12.903764109 x = 12.903764109 Simplifying x = 12.903764109Subproblem 2
x + -3.60000144 = -9.303762669 Simplifying x + -3.60000144 = -9.303762669 Reorder the terms: -3.60000144 + x = -9.303762669 Solving -3.60000144 + x = -9.303762669 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.60000144' to each side of the equation. -3.60000144 + 3.60000144 + x = -9.303762669 + 3.60000144 Combine like terms: -3.60000144 + 3.60000144 = 0.00000000 0.00000000 + x = -9.303762669 + 3.60000144 x = -9.303762669 + 3.60000144 Combine like terms: -9.303762669 + 3.60000144 = -5.703761229 x = -5.703761229 Simplifying x = -5.703761229Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.903764109, -5.703761229}
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