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Simplifying x2 + 16x = 276 Reorder the terms: 16x + x2 = 276 Solving 16x + x2 = 276 Solving for variable 'x'. Reorder the terms: -276 + 16x + x2 = 276 + -276 Combine like terms: 276 + -276 = 0 -276 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '276' to each side of the equation. -276 + 16x + 276 + x2 = 0 + 276 Reorder the terms: -276 + 276 + 16x + x2 = 0 + 276 Combine like terms: -276 + 276 = 0 0 + 16x + x2 = 0 + 276 16x + x2 = 0 + 276 Combine like terms: 0 + 276 = 276 16x + x2 = 276 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 = 276 + 64 Reorder the terms: 64 + 16x + x2 = 276 + 64 Combine like terms: 276 + 64 = 340 64 + 16x + x2 = 340 Factor a perfect square on the left side: (x + 8)(x + 8) = 340 Calculate the square root of the right side: 18.439088915 Break this problem into two subproblems by setting (x + 8) equal to 18.439088915 and -18.439088915.Subproblem 1
x + 8 = 18.439088915 Simplifying x + 8 = 18.439088915 Reorder the terms: 8 + x = 18.439088915 Solving 8 + x = 18.439088915 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 = 18.439088915 + -8 Combine like terms: 8 + -8 = 0 0 + x = 18.439088915 + -8 x = 18.439088915 + -8 Combine like terms: 18.439088915 + -8 = 10.439088915 x = 10.439088915 Simplifying x = 10.439088915Subproblem 2
x + 8 = -18.439088915 Simplifying x + 8 = -18.439088915 Reorder the terms: 8 + x = -18.439088915 Solving 8 + x = -18.439088915 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 = -18.439088915 + -8 Combine like terms: 8 + -8 = 0 0 + x = -18.439088915 + -8 x = -18.439088915 + -8 Combine like terms: -18.439088915 + -8 = -26.439088915 x = -26.439088915 Simplifying x = -26.439088915Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.439088915, -26.439088915}
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