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Simplifying 5x + x2 = 171 Solving 5x + x2 = 171 Solving for variable 'x'. Reorder the terms: -171 + 5x + x2 = 171 + -171 Combine like terms: 171 + -171 = 0 -171 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '171' to each side of the equation. -171 + 5x + 171 + x2 = 0 + 171 Reorder the terms: -171 + 171 + 5x + x2 = 0 + 171 Combine like terms: -171 + 171 = 0 0 + 5x + x2 = 0 + 171 5x + x2 = 0 + 171 Combine like terms: 0 + 171 = 171 5x + x2 = 171 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 = 171 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 171 + 6.25 Combine like terms: 171 + 6.25 = 177.25 6.25 + 5x + x2 = 177.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 177.25 Calculate the square root of the right side: 13.313526956 Break this problem into two subproblems by setting (x + 2.5) equal to 13.313526956 and -13.313526956.Subproblem 1
x + 2.5 = 13.313526956 Simplifying x + 2.5 = 13.313526956 Reorder the terms: 2.5 + x = 13.313526956 Solving 2.5 + x = 13.313526956 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 = 13.313526956 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 13.313526956 + -2.5 x = 13.313526956 + -2.5 Combine like terms: 13.313526956 + -2.5 = 10.813526956 x = 10.813526956 Simplifying x = 10.813526956Subproblem 2
x + 2.5 = -13.313526956 Simplifying x + 2.5 = -13.313526956 Reorder the terms: 2.5 + x = -13.313526956 Solving 2.5 + x = -13.313526956 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 = -13.313526956 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -13.313526956 + -2.5 x = -13.313526956 + -2.5 Combine like terms: -13.313526956 + -2.5 = -15.813526956 x = -15.813526956 Simplifying x = -15.813526956Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.813526956, -15.813526956}
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