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Simplifying x2 + -106x + 60 = 0 Reorder the terms: 60 + -106x + x2 = 0 Solving 60 + -106x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-60' to each side of the equation. 60 + -106x + -60 + x2 = 0 + -60 Reorder the terms: 60 + -60 + -106x + x2 = 0 + -60 Combine like terms: 60 + -60 = 0 0 + -106x + x2 = 0 + -60 -106x + x2 = 0 + -60 Combine like terms: 0 + -60 = -60 -106x + x2 = -60 The x term is -106x. Take half its coefficient (-53). Square it (2809) and add it to both sides. Add '2809' to each side of the equation. -106x + 2809 + x2 = -60 + 2809 Reorder the terms: 2809 + -106x + x2 = -60 + 2809 Combine like terms: -60 + 2809 = 2749 2809 + -106x + x2 = 2749 Factor a perfect square on the left side: (x + -53)(x + -53) = 2749 Calculate the square root of the right side: 52.430906916 Break this problem into two subproblems by setting (x + -53) equal to 52.430906916 and -52.430906916.Subproblem 1
x + -53 = 52.430906916 Simplifying x + -53 = 52.430906916 Reorder the terms: -53 + x = 52.430906916 Solving -53 + x = 52.430906916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '53' to each side of the equation. -53 + 53 + x = 52.430906916 + 53 Combine like terms: -53 + 53 = 0 0 + x = 52.430906916 + 53 x = 52.430906916 + 53 Combine like terms: 52.430906916 + 53 = 105.430906916 x = 105.430906916 Simplifying x = 105.430906916Subproblem 2
x + -53 = -52.430906916 Simplifying x + -53 = -52.430906916 Reorder the terms: -53 + x = -52.430906916 Solving -53 + x = -52.430906916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '53' to each side of the equation. -53 + 53 + x = -52.430906916 + 53 Combine like terms: -53 + 53 = 0 0 + x = -52.430906916 + 53 x = -52.430906916 + 53 Combine like terms: -52.430906916 + 53 = 0.569093084 x = 0.569093084 Simplifying x = 0.569093084Solution
The solution to the problem is based on the solutions from the subproblems. x = {105.430906916, 0.569093084}
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