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Simplifying x2 + 16x = -50 Reorder the terms: 16x + x2 = -50 Solving 16x + x2 = -50 Solving for variable 'x'. Reorder the terms: 50 + 16x + x2 = -50 + 50 Combine like terms: -50 + 50 = 0 50 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-50' to each side of the equation. 50 + 16x + -50 + x2 = 0 + -50 Reorder the terms: 50 + -50 + 16x + x2 = 0 + -50 Combine like terms: 50 + -50 = 0 0 + 16x + x2 = 0 + -50 16x + x2 = 0 + -50 Combine like terms: 0 + -50 = -50 16x + x2 = -50 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 = -50 + 64 Reorder the terms: 64 + 16x + x2 = -50 + 64 Combine like terms: -50 + 64 = 14 64 + 16x + x2 = 14 Factor a perfect square on the left side: (x + 8)(x + 8) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (x + 8) equal to 3.741657387 and -3.741657387.Subproblem 1
x + 8 = 3.741657387 Simplifying x + 8 = 3.741657387 Reorder the terms: 8 + x = 3.741657387 Solving 8 + x = 3.741657387 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 = 3.741657387 + -8 Combine like terms: 8 + -8 = 0 0 + x = 3.741657387 + -8 x = 3.741657387 + -8 Combine like terms: 3.741657387 + -8 = -4.258342613 x = -4.258342613 Simplifying x = -4.258342613Subproblem 2
x + 8 = -3.741657387 Simplifying x + 8 = -3.741657387 Reorder the terms: 8 + x = -3.741657387 Solving 8 + x = -3.741657387 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 = -3.741657387 + -8 Combine like terms: 8 + -8 = 0 0 + x = -3.741657387 + -8 x = -3.741657387 + -8 Combine like terms: -3.741657387 + -8 = -11.741657387 x = -11.741657387 Simplifying x = -11.741657387Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.258342613, -11.741657387}
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