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Simplifying x = 50 + 36x + -3x2 Solving x = 50 + 36x + -3x2 Solving for variable 'x'. Reorder the terms: -50 + x + -36x + 3x2 = 50 + 36x + -3x2 + -50 + -36x + 3x2 Combine like terms: x + -36x = -35x -50 + -35x + 3x2 = 50 + 36x + -3x2 + -50 + -36x + 3x2 Reorder the terms: -50 + -35x + 3x2 = 50 + -50 + 36x + -36x + -3x2 + 3x2 Combine like terms: 50 + -50 = 0 -50 + -35x + 3x2 = 0 + 36x + -36x + -3x2 + 3x2 -50 + -35x + 3x2 = 36x + -36x + -3x2 + 3x2 Combine like terms: 36x + -36x = 0 -50 + -35x + 3x2 = 0 + -3x2 + 3x2 -50 + -35x + 3x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 -50 + -35x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -16.66666667 + -11.66666667x + x2 = 0 Move the constant term to the right: Add '16.66666667' to each side of the equation. -16.66666667 + -11.66666667x + 16.66666667 + x2 = 0 + 16.66666667 Reorder the terms: -16.66666667 + 16.66666667 + -11.66666667x + x2 = 0 + 16.66666667 Combine like terms: -16.66666667 + 16.66666667 = 0.00000000 0.00000000 + -11.66666667x + x2 = 0 + 16.66666667 -11.66666667x + x2 = 0 + 16.66666667 Combine like terms: 0 + 16.66666667 = 16.66666667 -11.66666667x + x2 = 16.66666667 The x term is -11.66666667x. Take half its coefficient (-5.833333335). Square it (34.02777780) and add it to both sides. Add '34.02777780' to each side of the equation. -11.66666667x + 34.02777780 + x2 = 16.66666667 + 34.02777780 Reorder the terms: 34.02777780 + -11.66666667x + x2 = 16.66666667 + 34.02777780 Combine like terms: 16.66666667 + 34.02777780 = 50.69444447 34.02777780 + -11.66666667x + x2 = 50.69444447 Factor a perfect square on the left side: (x + -5.833333335)(x + -5.833333335) = 50.69444447 Calculate the square root of the right side: 7.120003123 Break this problem into two subproblems by setting (x + -5.833333335) equal to 7.120003123 and -7.120003123.Subproblem 1
x + -5.833333335 = 7.120003123 Simplifying x + -5.833333335 = 7.120003123 Reorder the terms: -5.833333335 + x = 7.120003123 Solving -5.833333335 + x = 7.120003123 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.833333335' to each side of the equation. -5.833333335 + 5.833333335 + x = 7.120003123 + 5.833333335 Combine like terms: -5.833333335 + 5.833333335 = 0.000000000 0.000000000 + x = 7.120003123 + 5.833333335 x = 7.120003123 + 5.833333335 Combine like terms: 7.120003123 + 5.833333335 = 12.953336458 x = 12.953336458 Simplifying x = 12.953336458Subproblem 2
x + -5.833333335 = -7.120003123 Simplifying x + -5.833333335 = -7.120003123 Reorder the terms: -5.833333335 + x = -7.120003123 Solving -5.833333335 + x = -7.120003123 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.833333335' to each side of the equation. -5.833333335 + 5.833333335 + x = -7.120003123 + 5.833333335 Combine like terms: -5.833333335 + 5.833333335 = 0.000000000 0.000000000 + x = -7.120003123 + 5.833333335 x = -7.120003123 + 5.833333335 Combine like terms: -7.120003123 + 5.833333335 = -1.286669788 x = -1.286669788 Simplifying x = -1.286669788Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.953336458, -1.286669788}
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