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Simplifying 5.56x2 + -6.05x = 2.76 Reorder the terms: -6.05x + 5.56x2 = 2.76 Solving -6.05x + 5.56x2 = 2.76 Solving for variable 'x'. Reorder the terms: -2.76 + -6.05x + 5.56x2 = 2.76 + -2.76 Combine like terms: 2.76 + -2.76 = 0.00 -2.76 + -6.05x + 5.56x2 = 0.00 Begin completing the square. Divide all terms by 5.56 the coefficient of the squared term: Divide each side by '5.56'. -0.4964028777 + -1.088129496x + x2 = 0 Move the constant term to the right: Add '0.4964028777' to each side of the equation. -0.4964028777 + -1.088129496x + 0.4964028777 + x2 = 0 + 0.4964028777 Reorder the terms: -0.4964028777 + 0.4964028777 + -1.088129496x + x2 = 0 + 0.4964028777 Combine like terms: -0.4964028777 + 0.4964028777 = 0.0000000000 0.0000000000 + -1.088129496x + x2 = 0 + 0.4964028777 -1.088129496x + x2 = 0 + 0.4964028777 Combine like terms: 0 + 0.4964028777 = 0.4964028777 -1.088129496x + x2 = 0.4964028777 The x term is -1.088129496x. Take half its coefficient (-0.544064748). Square it (0.2960064500) and add it to both sides. Add '0.2960064500' to each side of the equation. -1.088129496x + 0.2960064500 + x2 = 0.4964028777 + 0.2960064500 Reorder the terms: 0.2960064500 + -1.088129496x + x2 = 0.4964028777 + 0.2960064500 Combine like terms: 0.4964028777 + 0.2960064500 = 0.7924093277 0.2960064500 + -1.088129496x + x2 = 0.7924093277 Factor a perfect square on the left side: (x + -0.544064748)(x + -0.544064748) = 0.7924093277 Calculate the square root of the right side: 0.890173763 Break this problem into two subproblems by setting (x + -0.544064748) equal to 0.890173763 and -0.890173763.Subproblem 1
x + -0.544064748 = 0.890173763 Simplifying x + -0.544064748 = 0.890173763 Reorder the terms: -0.544064748 + x = 0.890173763 Solving -0.544064748 + x = 0.890173763 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.544064748' to each side of the equation. -0.544064748 + 0.544064748 + x = 0.890173763 + 0.544064748 Combine like terms: -0.544064748 + 0.544064748 = 0.000000000 0.000000000 + x = 0.890173763 + 0.544064748 x = 0.890173763 + 0.544064748 Combine like terms: 0.890173763 + 0.544064748 = 1.434238511 x = 1.434238511 Simplifying x = 1.434238511Subproblem 2
x + -0.544064748 = -0.890173763 Simplifying x + -0.544064748 = -0.890173763 Reorder the terms: -0.544064748 + x = -0.890173763 Solving -0.544064748 + x = -0.890173763 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.544064748' to each side of the equation. -0.544064748 + 0.544064748 + x = -0.890173763 + 0.544064748 Combine like terms: -0.544064748 + 0.544064748 = 0.000000000 0.000000000 + x = -0.890173763 + 0.544064748 x = -0.890173763 + 0.544064748 Combine like terms: -0.890173763 + 0.544064748 = -0.346109015 x = -0.346109015 Simplifying x = -0.346109015Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.434238511, -0.346109015}
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