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Simplifying x2 + -52x + 64 = 0 Reorder the terms: 64 + -52x + x2 = 0 Solving 64 + -52x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-64' to each side of the equation. 64 + -52x + -64 + x2 = 0 + -64 Reorder the terms: 64 + -64 + -52x + x2 = 0 + -64 Combine like terms: 64 + -64 = 0 0 + -52x + x2 = 0 + -64 -52x + x2 = 0 + -64 Combine like terms: 0 + -64 = -64 -52x + x2 = -64 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 = -64 + 676 Reorder the terms: 676 + -52x + x2 = -64 + 676 Combine like terms: -64 + 676 = 612 676 + -52x + x2 = 612 Factor a perfect square on the left side: (x + -26)(x + -26) = 612 Calculate the square root of the right side: 24.738633754 Break this problem into two subproblems by setting (x + -26) equal to 24.738633754 and -24.738633754.Subproblem 1
x + -26 = 24.738633754 Simplifying x + -26 = 24.738633754 Reorder the terms: -26 + x = 24.738633754 Solving -26 + x = 24.738633754 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 = 24.738633754 + 26 Combine like terms: -26 + 26 = 0 0 + x = 24.738633754 + 26 x = 24.738633754 + 26 Combine like terms: 24.738633754 + 26 = 50.738633754 x = 50.738633754 Simplifying x = 50.738633754Subproblem 2
x + -26 = -24.738633754 Simplifying x + -26 = -24.738633754 Reorder the terms: -26 + x = -24.738633754 Solving -26 + x = -24.738633754 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 = -24.738633754 + 26 Combine like terms: -26 + 26 = 0 0 + x = -24.738633754 + 26 x = -24.738633754 + 26 Combine like terms: -24.738633754 + 26 = 1.261366246 x = 1.261366246 Simplifying x = 1.261366246Solution
The solution to the problem is based on the solutions from the subproblems. x = {50.738633754, 1.261366246}
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