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Simplifying x2 + 8x + -160 = 0 Reorder the terms: -160 + 8x + x2 = 0 Solving -160 + 8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '160' to each side of the equation. -160 + 8x + 160 + x2 = 0 + 160 Reorder the terms: -160 + 160 + 8x + x2 = 0 + 160 Combine like terms: -160 + 160 = 0 0 + 8x + x2 = 0 + 160 8x + x2 = 0 + 160 Combine like terms: 0 + 160 = 160 8x + x2 = 160 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 160 + 16 Reorder the terms: 16 + 8x + x2 = 160 + 16 Combine like terms: 160 + 16 = 176 16 + 8x + x2 = 176 Factor a perfect square on the left side: (x + 4)(x + 4) = 176 Calculate the square root of the right side: 13.266499161 Break this problem into two subproblems by setting (x + 4) equal to 13.266499161 and -13.266499161.Subproblem 1
x + 4 = 13.266499161 Simplifying x + 4 = 13.266499161 Reorder the terms: 4 + x = 13.266499161 Solving 4 + x = 13.266499161 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 13.266499161 + -4 Combine like terms: 4 + -4 = 0 0 + x = 13.266499161 + -4 x = 13.266499161 + -4 Combine like terms: 13.266499161 + -4 = 9.266499161 x = 9.266499161 Simplifying x = 9.266499161Subproblem 2
x + 4 = -13.266499161 Simplifying x + 4 = -13.266499161 Reorder the terms: 4 + x = -13.266499161 Solving 4 + x = -13.266499161 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -13.266499161 + -4 Combine like terms: 4 + -4 = 0 0 + x = -13.266499161 + -4 x = -13.266499161 + -4 Combine like terms: -13.266499161 + -4 = -17.266499161 x = -17.266499161 Simplifying x = -17.266499161Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.266499161, -17.266499161}
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