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Simplifying 2(2x + -3) + 2(x + 4) + 12 + x2 = 78 Reorder the terms: 2(-3 + 2x) + 2(x + 4) + 12 + x2 = 78 (-3 * 2 + 2x * 2) + 2(x + 4) + 12 + x2 = 78 (-6 + 4x) + 2(x + 4) + 12 + x2 = 78 Reorder the terms: -6 + 4x + 2(4 + x) + 12 + x2 = 78 -6 + 4x + (4 * 2 + x * 2) + 12 + x2 = 78 -6 + 4x + (8 + 2x) + 12 + x2 = 78 Reorder the terms: -6 + 8 + 12 + 4x + 2x + x2 = 78 Combine like terms: -6 + 8 = 2 2 + 12 + 4x + 2x + x2 = 78 Combine like terms: 2 + 12 = 14 14 + 4x + 2x + x2 = 78 Combine like terms: 4x + 2x = 6x 14 + 6x + x2 = 78 Solving 14 + 6x + x2 = 78 Solving for variable 'x'. Reorder the terms: 14 + -78 + 6x + x2 = 78 + -78 Combine like terms: 14 + -78 = -64 -64 + 6x + x2 = 78 + -78 Combine like terms: 78 + -78 = 0 -64 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '64' to each side of the equation. -64 + 6x + 64 + x2 = 0 + 64 Reorder the terms: -64 + 64 + 6x + x2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + 6x + x2 = 0 + 64 6x + x2 = 0 + 64 Combine like terms: 0 + 64 = 64 6x + x2 = 64 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 = 64 + 9 Reorder the terms: 9 + 6x + x2 = 64 + 9 Combine like terms: 64 + 9 = 73 9 + 6x + x2 = 73 Factor a perfect square on the left side: (x + 3)(x + 3) = 73 Calculate the square root of the right side: 8.544003745 Break this problem into two subproblems by setting (x + 3) equal to 8.544003745 and -8.544003745.Subproblem 1
x + 3 = 8.544003745 Simplifying x + 3 = 8.544003745 Reorder the terms: 3 + x = 8.544003745 Solving 3 + x = 8.544003745 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 = 8.544003745 + -3 Combine like terms: 3 + -3 = 0 0 + x = 8.544003745 + -3 x = 8.544003745 + -3 Combine like terms: 8.544003745 + -3 = 5.544003745 x = 5.544003745 Simplifying x = 5.544003745Subproblem 2
x + 3 = -8.544003745 Simplifying x + 3 = -8.544003745 Reorder the terms: 3 + x = -8.544003745 Solving 3 + x = -8.544003745 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 = -8.544003745 + -3 Combine like terms: 3 + -3 = 0 0 + x = -8.544003745 + -3 x = -8.544003745 + -3 Combine like terms: -8.544003745 + -3 = -11.544003745 x = -11.544003745 Simplifying x = -11.544003745Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.544003745, -11.544003745}
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