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Simplifying x2 + -25x + 52 = 0 Reorder the terms: 52 + -25x + x2 = 0 Solving 52 + -25x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-52' to each side of the equation. 52 + -25x + -52 + x2 = 0 + -52 Reorder the terms: 52 + -52 + -25x + x2 = 0 + -52 Combine like terms: 52 + -52 = 0 0 + -25x + x2 = 0 + -52 -25x + x2 = 0 + -52 Combine like terms: 0 + -52 = -52 -25x + x2 = -52 The x term is -25x. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25x + 156.25 + x2 = -52 + 156.25 Reorder the terms: 156.25 + -25x + x2 = -52 + 156.25 Combine like terms: -52 + 156.25 = 104.25 156.25 + -25x + x2 = 104.25 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 104.25 Calculate the square root of the right side: 10.210288928 Break this problem into two subproblems by setting (x + -12.5) equal to 10.210288928 and -10.210288928.Subproblem 1
x + -12.5 = 10.210288928 Simplifying x + -12.5 = 10.210288928 Reorder the terms: -12.5 + x = 10.210288928 Solving -12.5 + x = 10.210288928 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = 10.210288928 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 10.210288928 + 12.5 x = 10.210288928 + 12.5 Combine like terms: 10.210288928 + 12.5 = 22.710288928 x = 22.710288928 Simplifying x = 22.710288928Subproblem 2
x + -12.5 = -10.210288928 Simplifying x + -12.5 = -10.210288928 Reorder the terms: -12.5 + x = -10.210288928 Solving -12.5 + x = -10.210288928 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = -10.210288928 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -10.210288928 + 12.5 x = -10.210288928 + 12.5 Combine like terms: -10.210288928 + 12.5 = 2.289711072 x = 2.289711072 Simplifying x = 2.289711072Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.710288928, 2.289711072}
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