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Simplifying x2 + -52x + 625 = 0 Reorder the terms: 625 + -52x + x2 = 0 Solving 625 + -52x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-625' to each side of the equation. 625 + -52x + -625 + x2 = 0 + -625 Reorder the terms: 625 + -625 + -52x + x2 = 0 + -625 Combine like terms: 625 + -625 = 0 0 + -52x + x2 = 0 + -625 -52x + x2 = 0 + -625 Combine like terms: 0 + -625 = -625 -52x + x2 = -625 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 = -625 + 676 Reorder the terms: 676 + -52x + x2 = -625 + 676 Combine like terms: -625 + 676 = 51 676 + -52x + x2 = 51 Factor a perfect square on the left side: (x + -26)(x + -26) = 51 Calculate the square root of the right side: 7.141428429 Break this problem into two subproblems by setting (x + -26) equal to 7.141428429 and -7.141428429.Subproblem 1
x + -26 = 7.141428429 Simplifying x + -26 = 7.141428429 Reorder the terms: -26 + x = 7.141428429 Solving -26 + x = 7.141428429 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 = 7.141428429 + 26 Combine like terms: -26 + 26 = 0 0 + x = 7.141428429 + 26 x = 7.141428429 + 26 Combine like terms: 7.141428429 + 26 = 33.141428429 x = 33.141428429 Simplifying x = 33.141428429Subproblem 2
x + -26 = -7.141428429 Simplifying x + -26 = -7.141428429 Reorder the terms: -26 + x = -7.141428429 Solving -26 + x = -7.141428429 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 = -7.141428429 + 26 Combine like terms: -26 + 26 = 0 0 + x = -7.141428429 + 26 x = -7.141428429 + 26 Combine like terms: -7.141428429 + 26 = 18.858571571 x = 18.858571571 Simplifying x = 18.858571571Solution
The solution to the problem is based on the solutions from the subproblems. x = {33.141428429, 18.858571571}
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