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Simplifying x2 + 16x = 234 Reorder the terms: 16x + x2 = 234 Solving 16x + x2 = 234 Solving for variable 'x'. Reorder the terms: -234 + 16x + x2 = 234 + -234 Combine like terms: 234 + -234 = 0 -234 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '234' to each side of the equation. -234 + 16x + 234 + x2 = 0 + 234 Reorder the terms: -234 + 234 + 16x + x2 = 0 + 234 Combine like terms: -234 + 234 = 0 0 + 16x + x2 = 0 + 234 16x + x2 = 0 + 234 Combine like terms: 0 + 234 = 234 16x + x2 = 234 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 = 234 + 64 Reorder the terms: 64 + 16x + x2 = 234 + 64 Combine like terms: 234 + 64 = 298 64 + 16x + x2 = 298 Factor a perfect square on the left side: (x + 8)(x + 8) = 298 Calculate the square root of the right side: 17.262676502 Break this problem into two subproblems by setting (x + 8) equal to 17.262676502 and -17.262676502.Subproblem 1
x + 8 = 17.262676502 Simplifying x + 8 = 17.262676502 Reorder the terms: 8 + x = 17.262676502 Solving 8 + x = 17.262676502 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 = 17.262676502 + -8 Combine like terms: 8 + -8 = 0 0 + x = 17.262676502 + -8 x = 17.262676502 + -8 Combine like terms: 17.262676502 + -8 = 9.262676502 x = 9.262676502 Simplifying x = 9.262676502Subproblem 2
x + 8 = -17.262676502 Simplifying x + 8 = -17.262676502 Reorder the terms: 8 + x = -17.262676502 Solving 8 + x = -17.262676502 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 = -17.262676502 + -8 Combine like terms: 8 + -8 = 0 0 + x = -17.262676502 + -8 x = -17.262676502 + -8 Combine like terms: -17.262676502 + -8 = -25.262676502 x = -25.262676502 Simplifying x = -25.262676502Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.262676502, -25.262676502}
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