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Simplifying (3 + 9) * x2 + 55x + 6 = 0 Combine like terms: 3 + 9 = 12 (12) * x2 + 55x + 6 = 0 Reorder the terms: 6 + 55x + 12x2 = 0 Solving 6 + 55x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.5 + 4.583333333x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + 4.583333333x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + 4.583333333x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + 4.583333333x + x2 = 0 + -0.5 4.583333333x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 4.583333333x + x2 = -0.5 The x term is 4.583333333x. Take half its coefficient (2.291666667). Square it (5.251736113) and add it to both sides. Add '5.251736113' to each side of the equation. 4.583333333x + 5.251736113 + x2 = -0.5 + 5.251736113 Reorder the terms: 5.251736113 + 4.583333333x + x2 = -0.5 + 5.251736113 Combine like terms: -0.5 + 5.251736113 = 4.751736113 5.251736113 + 4.583333333x + x2 = 4.751736113 Factor a perfect square on the left side: (x + 2.291666667)(x + 2.291666667) = 4.751736113 Calculate the square root of the right side: 2.179847727 Break this problem into two subproblems by setting (x + 2.291666667) equal to 2.179847727 and -2.179847727.Subproblem 1
x + 2.291666667 = 2.179847727 Simplifying x + 2.291666667 = 2.179847727 Reorder the terms: 2.291666667 + x = 2.179847727 Solving 2.291666667 + x = 2.179847727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.291666667' to each side of the equation. 2.291666667 + -2.291666667 + x = 2.179847727 + -2.291666667 Combine like terms: 2.291666667 + -2.291666667 = 0.000000000 0.000000000 + x = 2.179847727 + -2.291666667 x = 2.179847727 + -2.291666667 Combine like terms: 2.179847727 + -2.291666667 = -0.11181894 x = -0.11181894 Simplifying x = -0.11181894Subproblem 2
x + 2.291666667 = -2.179847727 Simplifying x + 2.291666667 = -2.179847727 Reorder the terms: 2.291666667 + x = -2.179847727 Solving 2.291666667 + x = -2.179847727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.291666667' to each side of the equation. 2.291666667 + -2.291666667 + x = -2.179847727 + -2.291666667 Combine like terms: 2.291666667 + -2.291666667 = 0.000000000 0.000000000 + x = -2.179847727 + -2.291666667 x = -2.179847727 + -2.291666667 Combine like terms: -2.179847727 + -2.291666667 = -4.471514394 x = -4.471514394 Simplifying x = -4.471514394Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.11181894, -4.471514394}
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