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Simplifying x2 + -52x + 165 = 0 Reorder the terms: 165 + -52x + x2 = 0 Solving 165 + -52x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-165' to each side of the equation. 165 + -52x + -165 + x2 = 0 + -165 Reorder the terms: 165 + -165 + -52x + x2 = 0 + -165 Combine like terms: 165 + -165 = 0 0 + -52x + x2 = 0 + -165 -52x + x2 = 0 + -165 Combine like terms: 0 + -165 = -165 -52x + x2 = -165 The x term is -52x. Take half its coefficient (-26). Square it (676) and add it to both sides. Add '676' to each side of the equation. -52x + 676 + x2 = -165 + 676 Reorder the terms: 676 + -52x + x2 = -165 + 676 Combine like terms: -165 + 676 = 511 676 + -52x + x2 = 511 Factor a perfect square on the left side: (x + -26)(x + -26) = 511 Calculate the square root of the right side: 22.605309111 Break this problem into two subproblems by setting (x + -26) equal to 22.605309111 and -22.605309111.Subproblem 1
x + -26 = 22.605309111 Simplifying x + -26 = 22.605309111 Reorder the terms: -26 + x = 22.605309111 Solving -26 + x = 22.605309111 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '26' to each side of the equation. -26 + 26 + x = 22.605309111 + 26 Combine like terms: -26 + 26 = 0 0 + x = 22.605309111 + 26 x = 22.605309111 + 26 Combine like terms: 22.605309111 + 26 = 48.605309111 x = 48.605309111 Simplifying x = 48.605309111Subproblem 2
x + -26 = -22.605309111 Simplifying x + -26 = -22.605309111 Reorder the terms: -26 + x = -22.605309111 Solving -26 + x = -22.605309111 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '26' to each side of the equation. -26 + 26 + x = -22.605309111 + 26 Combine like terms: -26 + 26 = 0 0 + x = -22.605309111 + 26 x = -22.605309111 + 26 Combine like terms: -22.605309111 + 26 = 3.394690889 x = 3.394690889 Simplifying x = 3.394690889Solution
The solution to the problem is based on the solutions from the subproblems. x = {48.605309111, 3.394690889}
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