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Simplifying 2x2 + 12x + 6 = x + -1 Reorder the terms: 6 + 12x + 2x2 = x + -1 Reorder the terms: 6 + 12x + 2x2 = -1 + x Solving 6 + 12x + 2x2 = -1 + x Solving for variable 'x'. Reorder the terms: 6 + 1 + 12x + -1x + 2x2 = -1 + x + 1 + -1x Combine like terms: 6 + 1 = 7 7 + 12x + -1x + 2x2 = -1 + x + 1 + -1x Combine like terms: 12x + -1x = 11x 7 + 11x + 2x2 = -1 + x + 1 + -1x Reorder the terms: 7 + 11x + 2x2 = -1 + 1 + x + -1x Combine like terms: -1 + 1 = 0 7 + 11x + 2x2 = 0 + x + -1x 7 + 11x + 2x2 = x + -1x Combine like terms: x + -1x = 0 7 + 11x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3.5 + 5.5x + x2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + 5.5x + -3.5 + x2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + 5.5x + x2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + 5.5x + x2 = 0 + -3.5 5.5x + x2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 5.5x + x2 = -3.5 The x term is 5.5x. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5x + 7.5625 + x2 = -3.5 + 7.5625 Reorder the terms: 7.5625 + 5.5x + x2 = -3.5 + 7.5625 Combine like terms: -3.5 + 7.5625 = 4.0625 7.5625 + 5.5x + x2 = 4.0625 Factor a perfect square on the left side: (x + 2.75)(x + 2.75) = 4.0625 Calculate the square root of the right side: 2.015564437 Break this problem into two subproblems by setting (x + 2.75) equal to 2.015564437 and -2.015564437.Subproblem 1
x + 2.75 = 2.015564437 Simplifying x + 2.75 = 2.015564437 Reorder the terms: 2.75 + x = 2.015564437 Solving 2.75 + x = 2.015564437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = 2.015564437 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = 2.015564437 + -2.75 x = 2.015564437 + -2.75 Combine like terms: 2.015564437 + -2.75 = -0.734435563 x = -0.734435563 Simplifying x = -0.734435563Subproblem 2
x + 2.75 = -2.015564437 Simplifying x + 2.75 = -2.015564437 Reorder the terms: 2.75 + x = -2.015564437 Solving 2.75 + x = -2.015564437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = -2.015564437 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = -2.015564437 + -2.75 x = -2.015564437 + -2.75 Combine like terms: -2.015564437 + -2.75 = -4.765564437 x = -4.765564437 Simplifying x = -4.765564437Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.734435563, -4.765564437}
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