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Simplifying x2 + -19x + 49 = 0 Reorder the terms: 49 + -19x + x2 = 0 Solving 49 + -19x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-49' to each side of the equation. 49 + -19x + -49 + x2 = 0 + -49 Reorder the terms: 49 + -49 + -19x + x2 = 0 + -49 Combine like terms: 49 + -49 = 0 0 + -19x + x2 = 0 + -49 -19x + x2 = 0 + -49 Combine like terms: 0 + -49 = -49 -19x + x2 = -49 The x term is -19x. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19x + 90.25 + x2 = -49 + 90.25 Reorder the terms: 90.25 + -19x + x2 = -49 + 90.25 Combine like terms: -49 + 90.25 = 41.25 90.25 + -19x + x2 = 41.25 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 41.25 Calculate the square root of the right side: 6.422616289 Break this problem into two subproblems by setting (x + -9.5) equal to 6.422616289 and -6.422616289.Subproblem 1
x + -9.5 = 6.422616289 Simplifying x + -9.5 = 6.422616289 Reorder the terms: -9.5 + x = 6.422616289 Solving -9.5 + x = 6.422616289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = 6.422616289 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 6.422616289 + 9.5 x = 6.422616289 + 9.5 Combine like terms: 6.422616289 + 9.5 = 15.922616289 x = 15.922616289 Simplifying x = 15.922616289Subproblem 2
x + -9.5 = -6.422616289 Simplifying x + -9.5 = -6.422616289 Reorder the terms: -9.5 + x = -6.422616289 Solving -9.5 + x = -6.422616289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = -6.422616289 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -6.422616289 + 9.5 x = -6.422616289 + 9.5 Combine like terms: -6.422616289 + 9.5 = 3.077383711 x = 3.077383711 Simplifying x = 3.077383711Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.922616289, 3.077383711}
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