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Simplifying 0 = 0.67x2 + 6x + -168 Reorder the terms: 0 = -168 + 6x + 0.67x2 Solving 0 = -168 + 6x + 0.67x2 Solving for variable 'x'. Combine like terms: 0 + 168 = 168 168 + -6x + -0.67x2 = -168 + 6x + 0.67x2 + 168 + -6x + -0.67x2 Reorder the terms: 168 + -6x + -0.67x2 = -168 + 168 + 6x + -6x + 0.67x2 + -0.67x2 Combine like terms: -168 + 168 = 0 168 + -6x + -0.67x2 = 0 + 6x + -6x + 0.67x2 + -0.67x2 168 + -6x + -0.67x2 = 6x + -6x + 0.67x2 + -0.67x2 Combine like terms: 6x + -6x = 0 168 + -6x + -0.67x2 = 0 + 0.67x2 + -0.67x2 168 + -6x + -0.67x2 = 0.67x2 + -0.67x2 Combine like terms: 0.67x2 + -0.67x2 = 0.00 168 + -6x + -0.67x2 = 0.00 Begin completing the square. Divide all terms by -0.67 the coefficient of the squared term: Divide each side by '-0.67'. -250.7462687 + 8.955223881x + x2 = 0 Move the constant term to the right: Add '250.7462687' to each side of the equation. -250.7462687 + 8.955223881x + 250.7462687 + x2 = 0 + 250.7462687 Reorder the terms: -250.7462687 + 250.7462687 + 8.955223881x + x2 = 0 + 250.7462687 Combine like terms: -250.7462687 + 250.7462687 = 0.0000000 0.0000000 + 8.955223881x + x2 = 0 + 250.7462687 8.955223881x + x2 = 0 + 250.7462687 Combine like terms: 0 + 250.7462687 = 250.7462687 8.955223881x + x2 = 250.7462687 The x term is 8.955223881x. Take half its coefficient (4.477611941). Square it (20.04900869) and add it to both sides. Add '20.04900869' to each side of the equation. 8.955223881x + 20.04900869 + x2 = 250.7462687 + 20.04900869 Reorder the terms: 20.04900869 + 8.955223881x + x2 = 250.7462687 + 20.04900869 Combine like terms: 250.7462687 + 20.04900869 = 270.79527739 20.04900869 + 8.955223881x + x2 = 270.79527739 Factor a perfect square on the left side: (x + 4.477611941)(x + 4.477611941) = 270.79527739 Calculate the square root of the right side: 16.455858452 Break this problem into two subproblems by setting (x + 4.477611941) equal to 16.455858452 and -16.455858452.Subproblem 1
x + 4.477611941 = 16.455858452 Simplifying x + 4.477611941 = 16.455858452 Reorder the terms: 4.477611941 + x = 16.455858452 Solving 4.477611941 + x = 16.455858452 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.477611941' to each side of the equation. 4.477611941 + -4.477611941 + x = 16.455858452 + -4.477611941 Combine like terms: 4.477611941 + -4.477611941 = 0.000000000 0.000000000 + x = 16.455858452 + -4.477611941 x = 16.455858452 + -4.477611941 Combine like terms: 16.455858452 + -4.477611941 = 11.978246511 x = 11.978246511 Simplifying x = 11.978246511Subproblem 2
x + 4.477611941 = -16.455858452 Simplifying x + 4.477611941 = -16.455858452 Reorder the terms: 4.477611941 + x = -16.455858452 Solving 4.477611941 + x = -16.455858452 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.477611941' to each side of the equation. 4.477611941 + -4.477611941 + x = -16.455858452 + -4.477611941 Combine like terms: 4.477611941 + -4.477611941 = 0.000000000 0.000000000 + x = -16.455858452 + -4.477611941 x = -16.455858452 + -4.477611941 Combine like terms: -16.455858452 + -4.477611941 = -20.933470393 x = -20.933470393 Simplifying x = -20.933470393Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.978246511, -20.933470393}
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