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Simplifying x2 + 6x + 9 = 166 Reorder the terms: 9 + 6x + x2 = 166 Solving 9 + 6x + x2 = 166 Solving for variable 'x'. Reorder the terms: 9 + -166 + 6x + x2 = 166 + -166 Combine like terms: 9 + -166 = -157 -157 + 6x + x2 = 166 + -166 Combine like terms: 166 + -166 = 0 -157 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '157' to each side of the equation. -157 + 6x + 157 + x2 = 0 + 157 Reorder the terms: -157 + 157 + 6x + x2 = 0 + 157 Combine like terms: -157 + 157 = 0 0 + 6x + x2 = 0 + 157 6x + x2 = 0 + 157 Combine like terms: 0 + 157 = 157 6x + x2 = 157 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 157 + 9 Reorder the terms: 9 + 6x + x2 = 157 + 9 Combine like terms: 157 + 9 = 166 9 + 6x + x2 = 166 Factor a perfect square on the left side: (x + 3)(x + 3) = 166 Calculate the square root of the right side: 12.884098727 Break this problem into two subproblems by setting (x + 3) equal to 12.884098727 and -12.884098727.Subproblem 1
x + 3 = 12.884098727 Simplifying x + 3 = 12.884098727 Reorder the terms: 3 + x = 12.884098727 Solving 3 + x = 12.884098727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 12.884098727 + -3 Combine like terms: 3 + -3 = 0 0 + x = 12.884098727 + -3 x = 12.884098727 + -3 Combine like terms: 12.884098727 + -3 = 9.884098727 x = 9.884098727 Simplifying x = 9.884098727Subproblem 2
x + 3 = -12.884098727 Simplifying x + 3 = -12.884098727 Reorder the terms: 3 + x = -12.884098727 Solving 3 + x = -12.884098727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -12.884098727 + -3 Combine like terms: 3 + -3 = 0 0 + x = -12.884098727 + -3 x = -12.884098727 + -3 Combine like terms: -12.884098727 + -3 = -15.884098727 x = -15.884098727 Simplifying x = -15.884098727Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.884098727, -15.884098727}
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