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Simplifying x2 + -49x + -180 = 0 Reorder the terms: -180 + -49x + x2 = 0 Solving -180 + -49x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '180' to each side of the equation. -180 + -49x + 180 + x2 = 0 + 180 Reorder the terms: -180 + 180 + -49x + x2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + -49x + x2 = 0 + 180 -49x + x2 = 0 + 180 Combine like terms: 0 + 180 = 180 -49x + x2 = 180 The x term is -49x. Take half its coefficient (-24.5). Square it (600.25) and add it to both sides. Add '600.25' to each side of the equation. -49x + 600.25 + x2 = 180 + 600.25 Reorder the terms: 600.25 + -49x + x2 = 180 + 600.25 Combine like terms: 180 + 600.25 = 780.25 600.25 + -49x + x2 = 780.25 Factor a perfect square on the left side: (x + -24.5)(x + -24.5) = 780.25 Calculate the square root of the right side: 27.932955447 Break this problem into two subproblems by setting (x + -24.5) equal to 27.932955447 and -27.932955447.Subproblem 1
x + -24.5 = 27.932955447 Simplifying x + -24.5 = 27.932955447 Reorder the terms: -24.5 + x = 27.932955447 Solving -24.5 + x = 27.932955447 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24.5' to each side of the equation. -24.5 + 24.5 + x = 27.932955447 + 24.5 Combine like terms: -24.5 + 24.5 = 0.0 0.0 + x = 27.932955447 + 24.5 x = 27.932955447 + 24.5 Combine like terms: 27.932955447 + 24.5 = 52.432955447 x = 52.432955447 Simplifying x = 52.432955447Subproblem 2
x + -24.5 = -27.932955447 Simplifying x + -24.5 = -27.932955447 Reorder the terms: -24.5 + x = -27.932955447 Solving -24.5 + x = -27.932955447 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24.5' to each side of the equation. -24.5 + 24.5 + x = -27.932955447 + 24.5 Combine like terms: -24.5 + 24.5 = 0.0 0.0 + x = -27.932955447 + 24.5 x = -27.932955447 + 24.5 Combine like terms: -27.932955447 + 24.5 = -3.432955447 x = -3.432955447 Simplifying x = -3.432955447Solution
The solution to the problem is based on the solutions from the subproblems. x = {52.432955447, -3.432955447}
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