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Simplifying x2 + -25x + 121 = 0 Reorder the terms: 121 + -25x + x2 = 0 Solving 121 + -25x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-121' to each side of the equation. 121 + -25x + -121 + x2 = 0 + -121 Reorder the terms: 121 + -121 + -25x + x2 = 0 + -121 Combine like terms: 121 + -121 = 0 0 + -25x + x2 = 0 + -121 -25x + x2 = 0 + -121 Combine like terms: 0 + -121 = -121 -25x + x2 = -121 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 = -121 + 156.25 Reorder the terms: 156.25 + -25x + x2 = -121 + 156.25 Combine like terms: -121 + 156.25 = 35.25 156.25 + -25x + x2 = 35.25 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 35.25 Calculate the square root of the right side: 5.937171044 Break this problem into two subproblems by setting (x + -12.5) equal to 5.937171044 and -5.937171044.Subproblem 1
x + -12.5 = 5.937171044 Simplifying x + -12.5 = 5.937171044 Reorder the terms: -12.5 + x = 5.937171044 Solving -12.5 + x = 5.937171044 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 = 5.937171044 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 5.937171044 + 12.5 x = 5.937171044 + 12.5 Combine like terms: 5.937171044 + 12.5 = 18.437171044 x = 18.437171044 Simplifying x = 18.437171044Subproblem 2
x + -12.5 = -5.937171044 Simplifying x + -12.5 = -5.937171044 Reorder the terms: -12.5 + x = -5.937171044 Solving -12.5 + x = -5.937171044 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 = -5.937171044 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -5.937171044 + 12.5 x = -5.937171044 + 12.5 Combine like terms: -5.937171044 + 12.5 = 6.562828956 x = 6.562828956 Simplifying x = 6.562828956Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.437171044, 6.562828956}
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