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Simplifying x2 + 16x = 13 Reorder the terms: 16x + x2 = 13 Solving 16x + x2 = 13 Solving for variable 'x'. Reorder the terms: -13 + 16x + x2 = 13 + -13 Combine like terms: 13 + -13 = 0 -13 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + 16x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + 16x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 16x + x2 = 0 + 13 16x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 16x + x2 = 13 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 = 13 + 64 Reorder the terms: 64 + 16x + x2 = 13 + 64 Combine like terms: 13 + 64 = 77 64 + 16x + x2 = 77 Factor a perfect square on the left side: (x + 8)(x + 8) = 77 Calculate the square root of the right side: 8.774964387 Break this problem into two subproblems by setting (x + 8) equal to 8.774964387 and -8.774964387.Subproblem 1
x + 8 = 8.774964387 Simplifying x + 8 = 8.774964387 Reorder the terms: 8 + x = 8.774964387 Solving 8 + x = 8.774964387 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 = 8.774964387 + -8 Combine like terms: 8 + -8 = 0 0 + x = 8.774964387 + -8 x = 8.774964387 + -8 Combine like terms: 8.774964387 + -8 = 0.774964387 x = 0.774964387 Simplifying x = 0.774964387Subproblem 2
x + 8 = -8.774964387 Simplifying x + 8 = -8.774964387 Reorder the terms: 8 + x = -8.774964387 Solving 8 + x = -8.774964387 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 = -8.774964387 + -8 Combine like terms: 8 + -8 = 0 0 + x = -8.774964387 + -8 x = -8.774964387 + -8 Combine like terms: -8.774964387 + -8 = -16.774964387 x = -16.774964387 Simplifying x = -16.774964387Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.774964387, -16.774964387}
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