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Simplifying 12x2 + -55x + -7 = 0 Reorder the terms: -7 + -55x + 12x2 = 0 Solving -7 + -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'. -0.5833333333 + -4.583333333x + x2 = 0 Move the constant term to the right: Add '0.5833333333' to each side of the equation. -0.5833333333 + -4.583333333x + 0.5833333333 + x2 = 0 + 0.5833333333 Reorder the terms: -0.5833333333 + 0.5833333333 + -4.583333333x + x2 = 0 + 0.5833333333 Combine like terms: -0.5833333333 + 0.5833333333 = 0.0000000000 0.0000000000 + -4.583333333x + x2 = 0 + 0.5833333333 -4.583333333x + x2 = 0 + 0.5833333333 Combine like terms: 0 + 0.5833333333 = 0.5833333333 -4.583333333x + x2 = 0.5833333333 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 = 0.5833333333 + 5.251736113 Reorder the terms: 5.251736113 + -4.583333333x + x2 = 0.5833333333 + 5.251736113 Combine like terms: 0.5833333333 + 5.251736113 = 5.8350694463 5.251736113 + -4.583333333x + x2 = 5.8350694463 Factor a perfect square on the left side: (x + -2.291666667)(x + -2.291666667) = 5.8350694463 Calculate the square root of the right side: 2.41558884 Break this problem into two subproblems by setting (x + -2.291666667) equal to 2.41558884 and -2.41558884.Subproblem 1
x + -2.291666667 = 2.41558884 Simplifying x + -2.291666667 = 2.41558884 Reorder the terms: -2.291666667 + x = 2.41558884 Solving -2.291666667 + x = 2.41558884 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 = 2.41558884 + 2.291666667 Combine like terms: -2.291666667 + 2.291666667 = 0.000000000 0.000000000 + x = 2.41558884 + 2.291666667 x = 2.41558884 + 2.291666667 Combine like terms: 2.41558884 + 2.291666667 = 4.707255507 x = 4.707255507 Simplifying x = 4.707255507Subproblem 2
x + -2.291666667 = -2.41558884 Simplifying x + -2.291666667 = -2.41558884 Reorder the terms: -2.291666667 + x = -2.41558884 Solving -2.291666667 + x = -2.41558884 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 = -2.41558884 + 2.291666667 Combine like terms: -2.291666667 + 2.291666667 = 0.000000000 0.000000000 + x = -2.41558884 + 2.291666667 x = -2.41558884 + 2.291666667 Combine like terms: -2.41558884 + 2.291666667 = -0.123922173 x = -0.123922173 Simplifying x = -0.123922173Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.707255507, -0.123922173}
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