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Simplifying 6X2 + 7.1X + -0.6 = 0 Reorder the terms: -0.6 + 7.1X + 6X2 = 0 Solving -0.6 + 7.1X + 6X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.1 + 1.183333333X + X2 = 0 Move the constant term to the right: Add '0.1' to each side of the equation. -0.1 + 1.183333333X + 0.1 + X2 = 0 + 0.1 Reorder the terms: -0.1 + 0.1 + 1.183333333X + X2 = 0 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + 1.183333333X + X2 = 0 + 0.1 1.183333333X + X2 = 0 + 0.1 Combine like terms: 0 + 0.1 = 0.1 1.183333333X + X2 = 0.1 The X term is 1.183333333X. Take half its coefficient (0.5916666665). Square it (0.3500694442) and add it to both sides. Add '0.3500694442' to each side of the equation. 1.183333333X + 0.3500694442 + X2 = 0.1 + 0.3500694442 Reorder the terms: 0.3500694442 + 1.183333333X + X2 = 0.1 + 0.3500694442 Combine like terms: 0.1 + 0.3500694442 = 0.4500694442 0.3500694442 + 1.183333333X + X2 = 0.4500694442 Factor a perfect square on the left side: (X + 0.5916666665)(X + 0.5916666665) = 0.4500694442 Calculate the square root of the right side: 0.670872152 Break this problem into two subproblems by setting (X + 0.5916666665) equal to 0.670872152 and -0.670872152.Subproblem 1
X + 0.5916666665 = 0.670872152 Simplifying X + 0.5916666665 = 0.670872152 Reorder the terms: 0.5916666665 + X = 0.670872152 Solving 0.5916666665 + X = 0.670872152 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.5916666665' to each side of the equation. 0.5916666665 + -0.5916666665 + X = 0.670872152 + -0.5916666665 Combine like terms: 0.5916666665 + -0.5916666665 = 0.0000000000 0.0000000000 + X = 0.670872152 + -0.5916666665 X = 0.670872152 + -0.5916666665 Combine like terms: 0.670872152 + -0.5916666665 = 0.0792054855 X = 0.0792054855 Simplifying X = 0.0792054855Subproblem 2
X + 0.5916666665 = -0.670872152 Simplifying X + 0.5916666665 = -0.670872152 Reorder the terms: 0.5916666665 + X = -0.670872152 Solving 0.5916666665 + X = -0.670872152 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.5916666665' to each side of the equation. 0.5916666665 + -0.5916666665 + X = -0.670872152 + -0.5916666665 Combine like terms: 0.5916666665 + -0.5916666665 = 0.0000000000 0.0000000000 + X = -0.670872152 + -0.5916666665 X = -0.670872152 + -0.5916666665 Combine like terms: -0.670872152 + -0.5916666665 = -1.2625388185 X = -1.2625388185 Simplifying X = -1.2625388185Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.0792054855, -1.2625388185}
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