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Simplifying 67x + x2 = 154 + 3x Solving 67x + x2 = 154 + 3x Solving for variable 'x'. Reorder the terms: -154 + 67x + -3x + x2 = 154 + 3x + -154 + -3x Combine like terms: 67x + -3x = 64x -154 + 64x + x2 = 154 + 3x + -154 + -3x Reorder the terms: -154 + 64x + x2 = 154 + -154 + 3x + -3x Combine like terms: 154 + -154 = 0 -154 + 64x + x2 = 0 + 3x + -3x -154 + 64x + x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -154 + 64x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '154' to each side of the equation. -154 + 64x + 154 + x2 = 0 + 154 Reorder the terms: -154 + 154 + 64x + x2 = 0 + 154 Combine like terms: -154 + 154 = 0 0 + 64x + x2 = 0 + 154 64x + x2 = 0 + 154 Combine like terms: 0 + 154 = 154 64x + x2 = 154 The x term is 64x. Take half its coefficient (32). Square it (1024) and add it to both sides. Add '1024' to each side of the equation. 64x + 1024 + x2 = 154 + 1024 Reorder the terms: 1024 + 64x + x2 = 154 + 1024 Combine like terms: 154 + 1024 = 1178 1024 + 64x + x2 = 1178 Factor a perfect square on the left side: (x + 32)(x + 32) = 1178 Calculate the square root of the right side: 34.322004603 Break this problem into two subproblems by setting (x + 32) equal to 34.322004603 and -34.322004603.Subproblem 1
x + 32 = 34.322004603 Simplifying x + 32 = 34.322004603 Reorder the terms: 32 + x = 34.322004603 Solving 32 + x = 34.322004603 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-32' to each side of the equation. 32 + -32 + x = 34.322004603 + -32 Combine like terms: 32 + -32 = 0 0 + x = 34.322004603 + -32 x = 34.322004603 + -32 Combine like terms: 34.322004603 + -32 = 2.322004603 x = 2.322004603 Simplifying x = 2.322004603Subproblem 2
x + 32 = -34.322004603 Simplifying x + 32 = -34.322004603 Reorder the terms: 32 + x = -34.322004603 Solving 32 + x = -34.322004603 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-32' to each side of the equation. 32 + -32 + x = -34.322004603 + -32 Combine like terms: 32 + -32 = 0 0 + x = -34.322004603 + -32 x = -34.322004603 + -32 Combine like terms: -34.322004603 + -32 = -66.322004603 x = -66.322004603 Simplifying x = -66.322004603Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.322004603, -66.322004603}
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