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Simplifying x2 + 16x + -166 = 0 Reorder the terms: -166 + 16x + x2 = 0 Solving -166 + 16x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '166' to each side of the equation. -166 + 16x + 166 + x2 = 0 + 166 Reorder the terms: -166 + 166 + 16x + x2 = 0 + 166 Combine like terms: -166 + 166 = 0 0 + 16x + x2 = 0 + 166 16x + x2 = 0 + 166 Combine like terms: 0 + 166 = 166 16x + x2 = 166 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 = 166 + 64 Reorder the terms: 64 + 16x + x2 = 166 + 64 Combine like terms: 166 + 64 = 230 64 + 16x + x2 = 230 Factor a perfect square on the left side: (x + 8)(x + 8) = 230 Calculate the square root of the right side: 15.165750888 Break this problem into two subproblems by setting (x + 8) equal to 15.165750888 and -15.165750888.Subproblem 1
x + 8 = 15.165750888 Simplifying x + 8 = 15.165750888 Reorder the terms: 8 + x = 15.165750888 Solving 8 + x = 15.165750888 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 = 15.165750888 + -8 Combine like terms: 8 + -8 = 0 0 + x = 15.165750888 + -8 x = 15.165750888 + -8 Combine like terms: 15.165750888 + -8 = 7.165750888 x = 7.165750888 Simplifying x = 7.165750888Subproblem 2
x + 8 = -15.165750888 Simplifying x + 8 = -15.165750888 Reorder the terms: 8 + x = -15.165750888 Solving 8 + x = -15.165750888 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 = -15.165750888 + -8 Combine like terms: 8 + -8 = 0 0 + x = -15.165750888 + -8 x = -15.165750888 + -8 Combine like terms: -15.165750888 + -8 = -23.165750888 x = -23.165750888 Simplifying x = -23.165750888Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.165750888, -23.165750888}
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