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Simplifying x2 + 16x = -20 Reorder the terms: 16x + x2 = -20 Solving 16x + x2 = -20 Solving for variable 'x'. Reorder the terms: 20 + 16x + x2 = -20 + 20 Combine like terms: -20 + 20 = 0 20 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-20' to each side of the equation. 20 + 16x + -20 + x2 = 0 + -20 Reorder the terms: 20 + -20 + 16x + x2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + 16x + x2 = 0 + -20 16x + x2 = 0 + -20 Combine like terms: 0 + -20 = -20 16x + x2 = -20 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 = -20 + 64 Reorder the terms: 64 + 16x + x2 = -20 + 64 Combine like terms: -20 + 64 = 44 64 + 16x + x2 = 44 Factor a perfect square on the left side: (x + 8)(x + 8) = 44 Calculate the square root of the right side: 6.633249581 Break this problem into two subproblems by setting (x + 8) equal to 6.633249581 and -6.633249581.Subproblem 1
x + 8 = 6.633249581 Simplifying x + 8 = 6.633249581 Reorder the terms: 8 + x = 6.633249581 Solving 8 + x = 6.633249581 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 = 6.633249581 + -8 Combine like terms: 8 + -8 = 0 0 + x = 6.633249581 + -8 x = 6.633249581 + -8 Combine like terms: 6.633249581 + -8 = -1.366750419 x = -1.366750419 Simplifying x = -1.366750419Subproblem 2
x + 8 = -6.633249581 Simplifying x + 8 = -6.633249581 Reorder the terms: 8 + x = -6.633249581 Solving 8 + x = -6.633249581 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 = -6.633249581 + -8 Combine like terms: 8 + -8 = 0 0 + x = -6.633249581 + -8 x = -6.633249581 + -8 Combine like terms: -6.633249581 + -8 = -14.633249581 x = -14.633249581 Simplifying x = -14.633249581Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.366750419, -14.633249581}
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