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Simplifying -0.0665x2 + 3.58x + 122 = 0 Reorder the terms: 122 + 3.58x + -0.0665x2 = 0 Solving 122 + 3.58x + -0.0665x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.0665 the coefficient of the squared term: Divide each side by '-0.0665'. -1834.586466 + -53.83458647x + x2 = 0 Move the constant term to the right: Add '1834.586466' to each side of the equation. -1834.586466 + -53.83458647x + 1834.586466 + x2 = 0 + 1834.586466 Reorder the terms: -1834.586466 + 1834.586466 + -53.83458647x + x2 = 0 + 1834.586466 Combine like terms: -1834.586466 + 1834.586466 = 0.000000 0.000000 + -53.83458647x + x2 = 0 + 1834.586466 -53.83458647x + x2 = 0 + 1834.586466 Combine like terms: 0 + 1834.586466 = 1834.586466 -53.83458647x + x2 = 1834.586466 The x term is -53.83458647x. Take half its coefficient (-26.91729324). Square it (724.5406754) and add it to both sides. Add '724.5406754' to each side of the equation. -53.83458647x + 724.5406754 + x2 = 1834.586466 + 724.5406754 Reorder the terms: 724.5406754 + -53.83458647x + x2 = 1834.586466 + 724.5406754 Combine like terms: 1834.586466 + 724.5406754 = 2559.1271414 724.5406754 + -53.83458647x + x2 = 2559.1271414 Factor a perfect square on the left side: (x + -26.91729324)(x + -26.91729324) = 2559.1271414 Calculate the square root of the right side: 50.587816136 Break this problem into two subproblems by setting (x + -26.91729324) equal to 50.587816136 and -50.587816136.Subproblem 1
x + -26.91729324 = 50.587816136 Simplifying x + -26.91729324 = 50.587816136 Reorder the terms: -26.91729324 + x = 50.587816136 Solving -26.91729324 + x = 50.587816136 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '26.91729324' to each side of the equation. -26.91729324 + 26.91729324 + x = 50.587816136 + 26.91729324 Combine like terms: -26.91729324 + 26.91729324 = 0.00000000 0.00000000 + x = 50.587816136 + 26.91729324 x = 50.587816136 + 26.91729324 Combine like terms: 50.587816136 + 26.91729324 = 77.505109376 x = 77.505109376 Simplifying x = 77.505109376Subproblem 2
x + -26.91729324 = -50.587816136 Simplifying x + -26.91729324 = -50.587816136 Reorder the terms: -26.91729324 + x = -50.587816136 Solving -26.91729324 + x = -50.587816136 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '26.91729324' to each side of the equation. -26.91729324 + 26.91729324 + x = -50.587816136 + 26.91729324 Combine like terms: -26.91729324 + 26.91729324 = 0.00000000 0.00000000 + x = -50.587816136 + 26.91729324 x = -50.587816136 + 26.91729324 Combine like terms: -50.587816136 + 26.91729324 = -23.670522896 x = -23.670522896 Simplifying x = -23.670522896Solution
The solution to the problem is based on the solutions from the subproblems. x = {77.505109376, -23.670522896}
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