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Simplifying x2 + -12.256x + -63.077 = 0 Reorder the terms: -63.077 + -12.256x + x2 = 0 Solving -63.077 + -12.256x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '63.077' to each side of the equation. -63.077 + -12.256x + 63.077 + x2 = 0 + 63.077 Reorder the terms: -63.077 + 63.077 + -12.256x + x2 = 0 + 63.077 Combine like terms: -63.077 + 63.077 = 0.000 0.000 + -12.256x + x2 = 0 + 63.077 -12.256x + x2 = 0 + 63.077 Combine like terms: 0 + 63.077 = 63.077 -12.256x + x2 = 63.077 The x term is -12.256x. Take half its coefficient (-6.128). Square it (37.552384) and add it to both sides. Add '37.552384' to each side of the equation. -12.256x + 37.552384 + x2 = 63.077 + 37.552384 Reorder the terms: 37.552384 + -12.256x + x2 = 63.077 + 37.552384 Combine like terms: 63.077 + 37.552384 = 100.629384 37.552384 + -12.256x + x2 = 100.629384 Factor a perfect square on the left side: (x + -6.128)(x + -6.128) = 100.629384 Calculate the square root of the right side: 10.03141984 Break this problem into two subproblems by setting (x + -6.128) equal to 10.03141984 and -10.03141984.Subproblem 1
x + -6.128 = 10.03141984 Simplifying x + -6.128 = 10.03141984 Reorder the terms: -6.128 + x = 10.03141984 Solving -6.128 + x = 10.03141984 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.128' to each side of the equation. -6.128 + 6.128 + x = 10.03141984 + 6.128 Combine like terms: -6.128 + 6.128 = 0.000 0.000 + x = 10.03141984 + 6.128 x = 10.03141984 + 6.128 Combine like terms: 10.03141984 + 6.128 = 16.15941984 x = 16.15941984 Simplifying x = 16.15941984Subproblem 2
x + -6.128 = -10.03141984 Simplifying x + -6.128 = -10.03141984 Reorder the terms: -6.128 + x = -10.03141984 Solving -6.128 + x = -10.03141984 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.128' to each side of the equation. -6.128 + 6.128 + x = -10.03141984 + 6.128 Combine like terms: -6.128 + 6.128 = 0.000 0.000 + x = -10.03141984 + 6.128 x = -10.03141984 + 6.128 Combine like terms: -10.03141984 + 6.128 = -3.90341984 x = -3.90341984 Simplifying x = -3.90341984Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.15941984, -3.90341984}
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