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Simplifying x2 + 16x + -170 = -2 + 5 Reorder the terms: -170 + 16x + x2 = -2 + 5 Combine like terms: -2 + 5 = 3 -170 + 16x + x2 = 3 Solving -170 + 16x + x2 = 3 Solving for variable 'x'. Reorder the terms: -170 + -3 + 16x + x2 = 3 + -3 Combine like terms: -170 + -3 = -173 -173 + 16x + x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -173 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '173' to each side of the equation. -173 + 16x + 173 + x2 = 0 + 173 Reorder the terms: -173 + 173 + 16x + x2 = 0 + 173 Combine like terms: -173 + 173 = 0 0 + 16x + x2 = 0 + 173 16x + x2 = 0 + 173 Combine like terms: 0 + 173 = 173 16x + x2 = 173 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 = 173 + 64 Reorder the terms: 64 + 16x + x2 = 173 + 64 Combine like terms: 173 + 64 = 237 64 + 16x + x2 = 237 Factor a perfect square on the left side: (x + 8)(x + 8) = 237 Calculate the square root of the right side: 15.394804318 Break this problem into two subproblems by setting (x + 8) equal to 15.394804318 and -15.394804318.Subproblem 1
x + 8 = 15.394804318 Simplifying x + 8 = 15.394804318 Reorder the terms: 8 + x = 15.394804318 Solving 8 + x = 15.394804318 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 = 15.394804318 + -8 Combine like terms: 8 + -8 = 0 0 + x = 15.394804318 + -8 x = 15.394804318 + -8 Combine like terms: 15.394804318 + -8 = 7.394804318 x = 7.394804318 Simplifying x = 7.394804318Subproblem 2
x + 8 = -15.394804318 Simplifying x + 8 = -15.394804318 Reorder the terms: 8 + x = -15.394804318 Solving 8 + x = -15.394804318 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 = -15.394804318 + -8 Combine like terms: 8 + -8 = 0 0 + x = -15.394804318 + -8 x = -15.394804318 + -8 Combine like terms: -15.394804318 + -8 = -23.394804318 x = -23.394804318 Simplifying x = -23.394804318Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.394804318, -23.394804318}
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