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Simplifying x2 + 14 + 5x = 180 Reorder the terms: 14 + 5x + x2 = 180 Solving 14 + 5x + x2 = 180 Solving for variable 'x'. Reorder the terms: 14 + -180 + 5x + x2 = 180 + -180 Combine like terms: 14 + -180 = -166 -166 + 5x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -166 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '166' to each side of the equation. -166 + 5x + 166 + x2 = 0 + 166 Reorder the terms: -166 + 166 + 5x + x2 = 0 + 166 Combine like terms: -166 + 166 = 0 0 + 5x + x2 = 0 + 166 5x + x2 = 0 + 166 Combine like terms: 0 + 166 = 166 5x + x2 = 166 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 166 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 166 + 6.25 Combine like terms: 166 + 6.25 = 172.25 6.25 + 5x + x2 = 172.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 172.25 Calculate the square root of the right side: 13.124404748 Break this problem into two subproblems by setting (x + 2.5) equal to 13.124404748 and -13.124404748.Subproblem 1
x + 2.5 = 13.124404748 Simplifying x + 2.5 = 13.124404748 Reorder the terms: 2.5 + x = 13.124404748 Solving 2.5 + x = 13.124404748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 13.124404748 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 13.124404748 + -2.5 x = 13.124404748 + -2.5 Combine like terms: 13.124404748 + -2.5 = 10.624404748 x = 10.624404748 Simplifying x = 10.624404748Subproblem 2
x + 2.5 = -13.124404748 Simplifying x + 2.5 = -13.124404748 Reorder the terms: 2.5 + x = -13.124404748 Solving 2.5 + x = -13.124404748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -13.124404748 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -13.124404748 + -2.5 x = -13.124404748 + -2.5 Combine like terms: -13.124404748 + -2.5 = -15.624404748 x = -15.624404748 Simplifying x = -15.624404748Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.624404748, -15.624404748}
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