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Simplifying 12x + -23 + -2 + x2 + 4x = 49 Reorder the terms: -23 + -2 + 12x + 4x + x2 = 49 Combine like terms: -23 + -2 = -25 -25 + 12x + 4x + x2 = 49 Combine like terms: 12x + 4x = 16x -25 + 16x + x2 = 49 Solving -25 + 16x + x2 = 49 Solving for variable 'x'. Reorder the terms: -25 + -49 + 16x + x2 = 49 + -49 Combine like terms: -25 + -49 = -74 -74 + 16x + x2 = 49 + -49 Combine like terms: 49 + -49 = 0 -74 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '74' to each side of the equation. -74 + 16x + 74 + x2 = 0 + 74 Reorder the terms: -74 + 74 + 16x + x2 = 0 + 74 Combine like terms: -74 + 74 = 0 0 + 16x + x2 = 0 + 74 16x + x2 = 0 + 74 Combine like terms: 0 + 74 = 74 16x + x2 = 74 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = 74 + 64 Reorder the terms: 64 + 16x + x2 = 74 + 64 Combine like terms: 74 + 64 = 138 64 + 16x + x2 = 138 Factor a perfect square on the left side: (x + 8)(x + 8) = 138 Calculate the square root of the right side: 11.747340124 Break this problem into two subproblems by setting (x + 8) equal to 11.747340124 and -11.747340124.Subproblem 1
x + 8 = 11.747340124 Simplifying x + 8 = 11.747340124 Reorder the terms: 8 + x = 11.747340124 Solving 8 + x = 11.747340124 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 11.747340124 + -8 Combine like terms: 8 + -8 = 0 0 + x = 11.747340124 + -8 x = 11.747340124 + -8 Combine like terms: 11.747340124 + -8 = 3.747340124 x = 3.747340124 Simplifying x = 3.747340124Subproblem 2
x + 8 = -11.747340124 Simplifying x + 8 = -11.747340124 Reorder the terms: 8 + x = -11.747340124 Solving 8 + x = -11.747340124 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -11.747340124 + -8 Combine like terms: 8 + -8 = 0 0 + x = -11.747340124 + -8 x = -11.747340124 + -8 Combine like terms: -11.747340124 + -8 = -19.747340124 x = -19.747340124 Simplifying x = -19.747340124Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.747340124, -19.747340124}
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