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Simplifying x2 + -25x + 19 = 0 Reorder the terms: 19 + -25x + x2 = 0 Solving 19 + -25x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-19' to each side of the equation. 19 + -25x + -19 + x2 = 0 + -19 Reorder the terms: 19 + -19 + -25x + x2 = 0 + -19 Combine like terms: 19 + -19 = 0 0 + -25x + x2 = 0 + -19 -25x + x2 = 0 + -19 Combine like terms: 0 + -19 = -19 -25x + x2 = -19 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 = -19 + 156.25 Reorder the terms: 156.25 + -25x + x2 = -19 + 156.25 Combine like terms: -19 + 156.25 = 137.25 156.25 + -25x + x2 = 137.25 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 137.25 Calculate the square root of the right side: 11.715374514 Break this problem into two subproblems by setting (x + -12.5) equal to 11.715374514 and -11.715374514.Subproblem 1
x + -12.5 = 11.715374514 Simplifying x + -12.5 = 11.715374514 Reorder the terms: -12.5 + x = 11.715374514 Solving -12.5 + x = 11.715374514 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 = 11.715374514 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 11.715374514 + 12.5 x = 11.715374514 + 12.5 Combine like terms: 11.715374514 + 12.5 = 24.215374514 x = 24.215374514 Simplifying x = 24.215374514Subproblem 2
x + -12.5 = -11.715374514 Simplifying x + -12.5 = -11.715374514 Reorder the terms: -12.5 + x = -11.715374514 Solving -12.5 + x = -11.715374514 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 = -11.715374514 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -11.715374514 + 12.5 x = -11.715374514 + 12.5 Combine like terms: -11.715374514 + 12.5 = 0.784625486 x = 0.784625486 Simplifying x = 0.784625486Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.215374514, 0.784625486}
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