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Simplifying x2 + 6x + 5 = 180 Reorder the terms: 5 + 6x + x2 = 180 Solving 5 + 6x + x2 = 180 Solving for variable 'x'. Reorder the terms: 5 + -180 + 6x + x2 = 180 + -180 Combine like terms: 5 + -180 = -175 -175 + 6x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -175 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '175' to each side of the equation. -175 + 6x + 175 + x2 = 0 + 175 Reorder the terms: -175 + 175 + 6x + x2 = 0 + 175 Combine like terms: -175 + 175 = 0 0 + 6x + x2 = 0 + 175 6x + x2 = 0 + 175 Combine like terms: 0 + 175 = 175 6x + x2 = 175 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 = 175 + 9 Reorder the terms: 9 + 6x + x2 = 175 + 9 Combine like terms: 175 + 9 = 184 9 + 6x + x2 = 184 Factor a perfect square on the left side: (x + 3)(x + 3) = 184 Calculate the square root of the right side: 13.564659966 Break this problem into two subproblems by setting (x + 3) equal to 13.564659966 and -13.564659966.Subproblem 1
x + 3 = 13.564659966 Simplifying x + 3 = 13.564659966 Reorder the terms: 3 + x = 13.564659966 Solving 3 + x = 13.564659966 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 = 13.564659966 + -3 Combine like terms: 3 + -3 = 0 0 + x = 13.564659966 + -3 x = 13.564659966 + -3 Combine like terms: 13.564659966 + -3 = 10.564659966 x = 10.564659966 Simplifying x = 10.564659966Subproblem 2
x + 3 = -13.564659966 Simplifying x + 3 = -13.564659966 Reorder the terms: 3 + x = -13.564659966 Solving 3 + x = -13.564659966 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 = -13.564659966 + -3 Combine like terms: 3 + -3 = 0 0 + x = -13.564659966 + -3 x = -13.564659966 + -3 Combine like terms: -13.564659966 + -3 = -16.564659966 x = -16.564659966 Simplifying x = -16.564659966Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.564659966, -16.564659966}
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