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Simplifying 2x2 + 2x + -12 = x2 + -4x + 6 Reorder the terms: -12 + 2x + 2x2 = x2 + -4x + 6 Reorder the terms: -12 + 2x + 2x2 = 6 + -4x + x2 Solving -12 + 2x + 2x2 = 6 + -4x + x2 Solving for variable 'x'. Reorder the terms: -12 + -6 + 2x + 4x + 2x2 + -1x2 = 6 + -4x + x2 + -6 + 4x + -1x2 Combine like terms: -12 + -6 = -18 -18 + 2x + 4x + 2x2 + -1x2 = 6 + -4x + x2 + -6 + 4x + -1x2 Combine like terms: 2x + 4x = 6x -18 + 6x + 2x2 + -1x2 = 6 + -4x + x2 + -6 + 4x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 -18 + 6x + 1x2 = 6 + -4x + x2 + -6 + 4x + -1x2 Reorder the terms: -18 + 6x + 1x2 = 6 + -6 + -4x + 4x + x2 + -1x2 Combine like terms: 6 + -6 = 0 -18 + 6x + 1x2 = 0 + -4x + 4x + x2 + -1x2 -18 + 6x + 1x2 = -4x + 4x + x2 + -1x2 Combine like terms: -4x + 4x = 0 -18 + 6x + 1x2 = 0 + x2 + -1x2 -18 + 6x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -18 + 6x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + 6x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + 6x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 6x + x2 = 0 + 18 6x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 6x + x2 = 18 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 18 + 9 Reorder the terms: 9 + 6x + x2 = 18 + 9 Combine like terms: 18 + 9 = 27 9 + 6x + x2 = 27 Factor a perfect square on the left side: (x + 3)(x + 3) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (x + 3) equal to 5.196152423 and -5.196152423.Subproblem 1
x + 3 = 5.196152423 Simplifying x + 3 = 5.196152423 Reorder the terms: 3 + x = 5.196152423 Solving 3 + x = 5.196152423 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 5.196152423 + -3 Combine like terms: 3 + -3 = 0 0 + x = 5.196152423 + -3 x = 5.196152423 + -3 Combine like terms: 5.196152423 + -3 = 2.196152423 x = 2.196152423 Simplifying x = 2.196152423Subproblem 2
x + 3 = -5.196152423 Simplifying x + 3 = -5.196152423 Reorder the terms: 3 + x = -5.196152423 Solving 3 + x = -5.196152423 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -5.196152423 + -3 Combine like terms: 3 + -3 = 0 0 + x = -5.196152423 + -3 x = -5.196152423 + -3 Combine like terms: -5.196152423 + -3 = -8.196152423 x = -8.196152423 Simplifying x = -8.196152423Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.196152423, -8.196152423}
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