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Simplifying x2 + -52x + 73 = 0 Reorder the terms: 73 + -52x + x2 = 0 Solving 73 + -52x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-73' to each side of the equation. 73 + -52x + -73 + x2 = 0 + -73 Reorder the terms: 73 + -73 + -52x + x2 = 0 + -73 Combine like terms: 73 + -73 = 0 0 + -52x + x2 = 0 + -73 -52x + x2 = 0 + -73 Combine like terms: 0 + -73 = -73 -52x + x2 = -73 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 = -73 + 676 Reorder the terms: 676 + -52x + x2 = -73 + 676 Combine like terms: -73 + 676 = 603 676 + -52x + x2 = 603 Factor a perfect square on the left side: (x + -26)(x + -26) = 603 Calculate the square root of the right side: 24.556058316 Break this problem into two subproblems by setting (x + -26) equal to 24.556058316 and -24.556058316.Subproblem 1
x + -26 = 24.556058316 Simplifying x + -26 = 24.556058316 Reorder the terms: -26 + x = 24.556058316 Solving -26 + x = 24.556058316 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 = 24.556058316 + 26 Combine like terms: -26 + 26 = 0 0 + x = 24.556058316 + 26 x = 24.556058316 + 26 Combine like terms: 24.556058316 + 26 = 50.556058316 x = 50.556058316 Simplifying x = 50.556058316Subproblem 2
x + -26 = -24.556058316 Simplifying x + -26 = -24.556058316 Reorder the terms: -26 + x = -24.556058316 Solving -26 + x = -24.556058316 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 = -24.556058316 + 26 Combine like terms: -26 + 26 = 0 0 + x = -24.556058316 + 26 x = -24.556058316 + 26 Combine like terms: -24.556058316 + 26 = 1.443941684 x = 1.443941684 Simplifying x = 1.443941684Solution
The solution to the problem is based on the solutions from the subproblems. x = {50.556058316, 1.443941684}
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