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Simplifying x2 + -25x + 72 = 0 Reorder the terms: 72 + -25x + x2 = 0 Solving 72 + -25x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-72' to each side of the equation. 72 + -25x + -72 + x2 = 0 + -72 Reorder the terms: 72 + -72 + -25x + x2 = 0 + -72 Combine like terms: 72 + -72 = 0 0 + -25x + x2 = 0 + -72 -25x + x2 = 0 + -72 Combine like terms: 0 + -72 = -72 -25x + x2 = -72 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 = -72 + 156.25 Reorder the terms: 156.25 + -25x + x2 = -72 + 156.25 Combine like terms: -72 + 156.25 = 84.25 156.25 + -25x + x2 = 84.25 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 84.25 Calculate the square root of the right side: 9.178779875 Break this problem into two subproblems by setting (x + -12.5) equal to 9.178779875 and -9.178779875.Subproblem 1
x + -12.5 = 9.178779875 Simplifying x + -12.5 = 9.178779875 Reorder the terms: -12.5 + x = 9.178779875 Solving -12.5 + x = 9.178779875 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 = 9.178779875 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 9.178779875 + 12.5 x = 9.178779875 + 12.5 Combine like terms: 9.178779875 + 12.5 = 21.678779875 x = 21.678779875 Simplifying x = 21.678779875Subproblem 2
x + -12.5 = -9.178779875 Simplifying x + -12.5 = -9.178779875 Reorder the terms: -12.5 + x = -9.178779875 Solving -12.5 + x = -9.178779875 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 = -9.178779875 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -9.178779875 + 12.5 x = -9.178779875 + 12.5 Combine like terms: -9.178779875 + 12.5 = 3.321220125 x = 3.321220125 Simplifying x = 3.321220125Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.678779875, 3.321220125}
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