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Simplifying x2 + 64x + -121 = 0 Reorder the terms: -121 + 64x + x2 = 0 Solving -121 + 64x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '121' to each side of the equation. -121 + 64x + 121 + x2 = 0 + 121 Reorder the terms: -121 + 121 + 64x + x2 = 0 + 121 Combine like terms: -121 + 121 = 0 0 + 64x + x2 = 0 + 121 64x + x2 = 0 + 121 Combine like terms: 0 + 121 = 121 64x + x2 = 121 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 = 121 + 1024 Reorder the terms: 1024 + 64x + x2 = 121 + 1024 Combine like terms: 121 + 1024 = 1145 1024 + 64x + x2 = 1145 Factor a perfect square on the left side: (x + 32)(x + 32) = 1145 Calculate the square root of the right side: 33.837848631 Break this problem into two subproblems by setting (x + 32) equal to 33.837848631 and -33.837848631.Subproblem 1
x + 32 = 33.837848631 Simplifying x + 32 = 33.837848631 Reorder the terms: 32 + x = 33.837848631 Solving 32 + x = 33.837848631 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 = 33.837848631 + -32 Combine like terms: 32 + -32 = 0 0 + x = 33.837848631 + -32 x = 33.837848631 + -32 Combine like terms: 33.837848631 + -32 = 1.837848631 x = 1.837848631 Simplifying x = 1.837848631Subproblem 2
x + 32 = -33.837848631 Simplifying x + 32 = -33.837848631 Reorder the terms: 32 + x = -33.837848631 Solving 32 + x = -33.837848631 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 = -33.837848631 + -32 Combine like terms: 32 + -32 = 0 0 + x = -33.837848631 + -32 x = -33.837848631 + -32 Combine like terms: -33.837848631 + -32 = -65.837848631 x = -65.837848631 Simplifying x = -65.837848631Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.837848631, -65.837848631}
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