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Simplifying 3x2 + -11.2x + 2.7 = 0 Reorder the terms: 2.7 + -11.2x + 3x2 = 0 Solving 2.7 + -11.2x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.9 + -3.733333333x + x2 = 0 Move the constant term to the right: Add '-0.9' to each side of the equation. 0.9 + -3.733333333x + -0.9 + x2 = 0 + -0.9 Reorder the terms: 0.9 + -0.9 + -3.733333333x + x2 = 0 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + -3.733333333x + x2 = 0 + -0.9 -3.733333333x + x2 = 0 + -0.9 Combine like terms: 0 + -0.9 = -0.9 -3.733333333x + x2 = -0.9 The x term is -3.733333333x. Take half its coefficient (-1.866666667). Square it (3.484444446) and add it to both sides. Add '3.484444446' to each side of the equation. -3.733333333x + 3.484444446 + x2 = -0.9 + 3.484444446 Reorder the terms: 3.484444446 + -3.733333333x + x2 = -0.9 + 3.484444446 Combine like terms: -0.9 + 3.484444446 = 2.584444446 3.484444446 + -3.733333333x + x2 = 2.584444446 Factor a perfect square on the left side: (x + -1.866666667)(x + -1.866666667) = 2.584444446 Calculate the square root of the right side: 1.607620741 Break this problem into two subproblems by setting (x + -1.866666667) equal to 1.607620741 and -1.607620741.Subproblem 1
x + -1.866666667 = 1.607620741 Simplifying x + -1.866666667 = 1.607620741 Reorder the terms: -1.866666667 + x = 1.607620741 Solving -1.866666667 + x = 1.607620741 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.866666667' to each side of the equation. -1.866666667 + 1.866666667 + x = 1.607620741 + 1.866666667 Combine like terms: -1.866666667 + 1.866666667 = 0.000000000 0.000000000 + x = 1.607620741 + 1.866666667 x = 1.607620741 + 1.866666667 Combine like terms: 1.607620741 + 1.866666667 = 3.474287408 x = 3.474287408 Simplifying x = 3.474287408Subproblem 2
x + -1.866666667 = -1.607620741 Simplifying x + -1.866666667 = -1.607620741 Reorder the terms: -1.866666667 + x = -1.607620741 Solving -1.866666667 + x = -1.607620741 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.866666667' to each side of the equation. -1.866666667 + 1.866666667 + x = -1.607620741 + 1.866666667 Combine like terms: -1.866666667 + 1.866666667 = 0.000000000 0.000000000 + x = -1.607620741 + 1.866666667 x = -1.607620741 + 1.866666667 Combine like terms: -1.607620741 + 1.866666667 = 0.259045926 x = 0.259045926 Simplifying x = 0.259045926Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.474287408, 0.259045926}
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