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Simplifying x2 + -6x + -625 = 0 Reorder the terms: -625 + -6x + x2 = 0 Solving -625 + -6x + 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 + -6x + 625 + x2 = 0 + 625 Reorder the terms: -625 + 625 + -6x + x2 = 0 + 625 Combine like terms: -625 + 625 = 0 0 + -6x + x2 = 0 + 625 -6x + x2 = 0 + 625 Combine like terms: 0 + 625 = 625 -6x + x2 = 625 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 625 + 9 Reorder the terms: 9 + -6x + x2 = 625 + 9 Combine like terms: 625 + 9 = 634 9 + -6x + x2 = 634 Factor a perfect square on the left side: (x + -3)(x + -3) = 634 Calculate the square root of the right side: 25.179356624 Break this problem into two subproblems by setting (x + -3) equal to 25.179356624 and -25.179356624.Subproblem 1
x + -3 = 25.179356624 Simplifying x + -3 = 25.179356624 Reorder the terms: -3 + x = 25.179356624 Solving -3 + x = 25.179356624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 25.179356624 + 3 Combine like terms: -3 + 3 = 0 0 + x = 25.179356624 + 3 x = 25.179356624 + 3 Combine like terms: 25.179356624 + 3 = 28.179356624 x = 28.179356624 Simplifying x = 28.179356624Subproblem 2
x + -3 = -25.179356624 Simplifying x + -3 = -25.179356624 Reorder the terms: -3 + x = -25.179356624 Solving -3 + x = -25.179356624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -25.179356624 + 3 Combine like terms: -3 + 3 = 0 0 + x = -25.179356624 + 3 x = -25.179356624 + 3 Combine like terms: -25.179356624 + 3 = -22.179356624 x = -22.179356624 Simplifying x = -22.179356624Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.179356624, -22.179356624}
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