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Simplifying x2 + 6x + x + 14 = 180 Reorder the terms: 14 + 6x + x + x2 = 180 Combine like terms: 6x + x = 7x 14 + 7x + x2 = 180 Solving 14 + 7x + x2 = 180 Solving for variable 'x'. Reorder the terms: 14 + -180 + 7x + x2 = 180 + -180 Combine like terms: 14 + -180 = -166 -166 + 7x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -166 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '166' to each side of the equation. -166 + 7x + 166 + x2 = 0 + 166 Reorder the terms: -166 + 166 + 7x + x2 = 0 + 166 Combine like terms: -166 + 166 = 0 0 + 7x + x2 = 0 + 166 7x + x2 = 0 + 166 Combine like terms: 0 + 166 = 166 7x + x2 = 166 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 166 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 166 + 12.25 Combine like terms: 166 + 12.25 = 178.25 12.25 + 7x + x2 = 178.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 178.25 Calculate the square root of the right side: 13.351029923 Break this problem into two subproblems by setting (x + 3.5) equal to 13.351029923 and -13.351029923.Subproblem 1
x + 3.5 = 13.351029923 Simplifying x + 3.5 = 13.351029923 Reorder the terms: 3.5 + x = 13.351029923 Solving 3.5 + x = 13.351029923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 13.351029923 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 13.351029923 + -3.5 x = 13.351029923 + -3.5 Combine like terms: 13.351029923 + -3.5 = 9.851029923 x = 9.851029923 Simplifying x = 9.851029923Subproblem 2
x + 3.5 = -13.351029923 Simplifying x + 3.5 = -13.351029923 Reorder the terms: 3.5 + x = -13.351029923 Solving 3.5 + x = -13.351029923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -13.351029923 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -13.351029923 + -3.5 x = -13.351029923 + -3.5 Combine like terms: -13.351029923 + -3.5 = -16.851029923 x = -16.851029923 Simplifying x = -16.851029923Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.851029923, -16.851029923}
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