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Simplifying 0 = 36x2 + -480x + -2459 Reorder the terms: 0 = -2459 + -480x + 36x2 Solving 0 = -2459 + -480x + 36x2 Solving for variable 'x'. Combine like terms: 0 + 2459 = 2459 2459 + 480x + -36x2 = -2459 + -480x + 36x2 + 2459 + 480x + -36x2 Reorder the terms: 2459 + 480x + -36x2 = -2459 + 2459 + -480x + 480x + 36x2 + -36x2 Combine like terms: -2459 + 2459 = 0 2459 + 480x + -36x2 = 0 + -480x + 480x + 36x2 + -36x2 2459 + 480x + -36x2 = -480x + 480x + 36x2 + -36x2 Combine like terms: -480x + 480x = 0 2459 + 480x + -36x2 = 0 + 36x2 + -36x2 2459 + 480x + -36x2 = 36x2 + -36x2 Combine like terms: 36x2 + -36x2 = 0 2459 + 480x + -36x2 = 0 Begin completing the square. Divide all terms by -36 the coefficient of the squared term: Divide each side by '-36'. -68.30555556 + -13.33333333x + x2 = 0 Move the constant term to the right: Add '68.30555556' to each side of the equation. -68.30555556 + -13.33333333x + 68.30555556 + x2 = 0 + 68.30555556 Reorder the terms: -68.30555556 + 68.30555556 + -13.33333333x + x2 = 0 + 68.30555556 Combine like terms: -68.30555556 + 68.30555556 = 0.00000000 0.00000000 + -13.33333333x + x2 = 0 + 68.30555556 -13.33333333x + x2 = 0 + 68.30555556 Combine like terms: 0 + 68.30555556 = 68.30555556 -13.33333333x + x2 = 68.30555556 The x term is -13.33333333x. Take half its coefficient (-6.666666665). Square it (44.44444442) and add it to both sides. Add '44.44444442' to each side of the equation. -13.33333333x + 44.44444442 + x2 = 68.30555556 + 44.44444442 Reorder the terms: 44.44444442 + -13.33333333x + x2 = 68.30555556 + 44.44444442 Combine like terms: 68.30555556 + 44.44444442 = 112.74999998 44.44444442 + -13.33333333x + x2 = 112.74999998 Factor a perfect square on the left side: (x + -6.666666665)(x + -6.666666665) = 112.74999998 Calculate the square root of the right side: 10.61838029 Break this problem into two subproblems by setting (x + -6.666666665) equal to 10.61838029 and -10.61838029.Subproblem 1
x + -6.666666665 = 10.61838029 Simplifying x + -6.666666665 = 10.61838029 Reorder the terms: -6.666666665 + x = 10.61838029 Solving -6.666666665 + x = 10.61838029 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.666666665' to each side of the equation. -6.666666665 + 6.666666665 + x = 10.61838029 + 6.666666665 Combine like terms: -6.666666665 + 6.666666665 = 0.000000000 0.000000000 + x = 10.61838029 + 6.666666665 x = 10.61838029 + 6.666666665 Combine like terms: 10.61838029 + 6.666666665 = 17.285046955 x = 17.285046955 Simplifying x = 17.285046955Subproblem 2
x + -6.666666665 = -10.61838029 Simplifying x + -6.666666665 = -10.61838029 Reorder the terms: -6.666666665 + x = -10.61838029 Solving -6.666666665 + x = -10.61838029 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.666666665' to each side of the equation. -6.666666665 + 6.666666665 + x = -10.61838029 + 6.666666665 Combine like terms: -6.666666665 + 6.666666665 = 0.000000000 0.000000000 + x = -10.61838029 + 6.666666665 x = -10.61838029 + 6.666666665 Combine like terms: -10.61838029 + 6.666666665 = -3.951713625 x = -3.951713625 Simplifying x = -3.951713625Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.285046955, -3.951713625}
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