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Simplifying x2 + -625x + -256 = 0 Reorder the terms: -256 + -625x + x2 = 0 Solving -256 + -625x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '256' to each side of the equation. -256 + -625x + 256 + x2 = 0 + 256 Reorder the terms: -256 + 256 + -625x + x2 = 0 + 256 Combine like terms: -256 + 256 = 0 0 + -625x + x2 = 0 + 256 -625x + x2 = 0 + 256 Combine like terms: 0 + 256 = 256 -625x + x2 = 256 The x term is -625x. Take half its coefficient (-312.5). Square it (97656.25) and add it to both sides. Add '97656.25' to each side of the equation. -625x + 97656.25 + x2 = 256 + 97656.25 Reorder the terms: 97656.25 + -625x + x2 = 256 + 97656.25 Combine like terms: 256 + 97656.25 = 97912.25 97656.25 + -625x + x2 = 97912.25 Factor a perfect square on the left side: (x + -312.5)(x + -312.5) = 97912.25 Calculate the square root of the right side: 312.909331916 Break this problem into two subproblems by setting (x + -312.5) equal to 312.909331916 and -312.909331916.Subproblem 1
x + -312.5 = 312.909331916 Simplifying x + -312.5 = 312.909331916 Reorder the terms: -312.5 + x = 312.909331916 Solving -312.5 + x = 312.909331916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '312.5' to each side of the equation. -312.5 + 312.5 + x = 312.909331916 + 312.5 Combine like terms: -312.5 + 312.5 = 0.0 0.0 + x = 312.909331916 + 312.5 x = 312.909331916 + 312.5 Combine like terms: 312.909331916 + 312.5 = 625.409331916 x = 625.409331916 Simplifying x = 625.409331916Subproblem 2
x + -312.5 = -312.909331916 Simplifying x + -312.5 = -312.909331916 Reorder the terms: -312.5 + x = -312.909331916 Solving -312.5 + x = -312.909331916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '312.5' to each side of the equation. -312.5 + 312.5 + x = -312.909331916 + 312.5 Combine like terms: -312.5 + 312.5 = 0.0 0.0 + x = -312.909331916 + 312.5 x = -312.909331916 + 312.5 Combine like terms: -312.909331916 + 312.5 = -0.409331916 x = -0.409331916 Simplifying x = -0.409331916Solution
The solution to the problem is based on the solutions from the subproblems. x = {625.409331916, -0.409331916}
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