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Simplifying -0.059x2 + 2.6x + 35 = 0 Reorder the terms: 35 + 2.6x + -0.059x2 = 0 Solving 35 + 2.6x + -0.059x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.059 the coefficient of the squared term: Divide each side by '-0.059'. -593.220339 + -44.06779661x + x2 = 0 Move the constant term to the right: Add '593.220339' to each side of the equation. -593.220339 + -44.06779661x + 593.220339 + x2 = 0 + 593.220339 Reorder the terms: -593.220339 + 593.220339 + -44.06779661x + x2 = 0 + 593.220339 Combine like terms: -593.220339 + 593.220339 = 0.000000 0.000000 + -44.06779661x + x2 = 0 + 593.220339 -44.06779661x + x2 = 0 + 593.220339 Combine like terms: 0 + 593.220339 = 593.220339 -44.06779661x + x2 = 593.220339 The x term is -44.06779661x. Take half its coefficient (-22.03389831). Square it (485.4926747) and add it to both sides. Add '485.4926747' to each side of the equation. -44.06779661x + 485.4926747 + x2 = 593.220339 + 485.4926747 Reorder the terms: 485.4926747 + -44.06779661x + x2 = 593.220339 + 485.4926747 Combine like terms: 593.220339 + 485.4926747 = 1078.7130137 485.4926747 + -44.06779661x + x2 = 1078.7130137 Factor a perfect square on the left side: (x + -22.03389831)(x + -22.03389831) = 1078.7130137 Calculate the square root of the right side: 32.84376674 Break this problem into two subproblems by setting (x + -22.03389831) equal to 32.84376674 and -32.84376674.Subproblem 1
x + -22.03389831 = 32.84376674 Simplifying x + -22.03389831 = 32.84376674 Reorder the terms: -22.03389831 + x = 32.84376674 Solving -22.03389831 + x = 32.84376674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22.03389831' to each side of the equation. -22.03389831 + 22.03389831 + x = 32.84376674 + 22.03389831 Combine like terms: -22.03389831 + 22.03389831 = 0.00000000 0.00000000 + x = 32.84376674 + 22.03389831 x = 32.84376674 + 22.03389831 Combine like terms: 32.84376674 + 22.03389831 = 54.87766505 x = 54.87766505 Simplifying x = 54.87766505Subproblem 2
x + -22.03389831 = -32.84376674 Simplifying x + -22.03389831 = -32.84376674 Reorder the terms: -22.03389831 + x = -32.84376674 Solving -22.03389831 + x = -32.84376674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22.03389831' to each side of the equation. -22.03389831 + 22.03389831 + x = -32.84376674 + 22.03389831 Combine like terms: -22.03389831 + 22.03389831 = 0.00000000 0.00000000 + x = -32.84376674 + 22.03389831 x = -32.84376674 + 22.03389831 Combine like terms: -32.84376674 + 22.03389831 = -10.80986843 x = -10.80986843 Simplifying x = -10.80986843Solution
The solution to the problem is based on the solutions from the subproblems. x = {54.87766505, -10.80986843}
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