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Simplifying 36x2 + -482x + -2463 = 0 Reorder the terms: -2463 + -482x + 36x2 = 0 Solving -2463 + -482x + 36x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -68.41666667 + -13.38888889x + x2 = 0 Move the constant term to the right: Add '68.41666667' to each side of the equation. -68.41666667 + -13.38888889x + 68.41666667 + x2 = 0 + 68.41666667 Reorder the terms: -68.41666667 + 68.41666667 + -13.38888889x + x2 = 0 + 68.41666667 Combine like terms: -68.41666667 + 68.41666667 = 0.00000000 0.00000000 + -13.38888889x + x2 = 0 + 68.41666667 -13.38888889x + x2 = 0 + 68.41666667 Combine like terms: 0 + 68.41666667 = 68.41666667 -13.38888889x + x2 = 68.41666667 The x term is -13.38888889x. Take half its coefficient (-6.694444445). Square it (44.81558643) and add it to both sides. Add '44.81558643' to each side of the equation. -13.38888889x + 44.81558643 + x2 = 68.41666667 + 44.81558643 Reorder the terms: 44.81558643 + -13.38888889x + x2 = 68.41666667 + 44.81558643 Combine like terms: 68.41666667 + 44.81558643 = 113.2322531 44.81558643 + -13.38888889x + x2 = 113.2322531 Factor a perfect square on the left side: (x + -6.694444445)(x + -6.694444445) = 113.2322531 Calculate the square root of the right side: 10.641064472 Break this problem into two subproblems by setting (x + -6.694444445) equal to 10.641064472 and -10.641064472.Subproblem 1
x + -6.694444445 = 10.641064472 Simplifying x + -6.694444445 = 10.641064472 Reorder the terms: -6.694444445 + x = 10.641064472 Solving -6.694444445 + x = 10.641064472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.694444445' to each side of the equation. -6.694444445 + 6.694444445 + x = 10.641064472 + 6.694444445 Combine like terms: -6.694444445 + 6.694444445 = 0.000000000 0.000000000 + x = 10.641064472 + 6.694444445 x = 10.641064472 + 6.694444445 Combine like terms: 10.641064472 + 6.694444445 = 17.335508917 x = 17.335508917 Simplifying x = 17.335508917Subproblem 2
x + -6.694444445 = -10.641064472 Simplifying x + -6.694444445 = -10.641064472 Reorder the terms: -6.694444445 + x = -10.641064472 Solving -6.694444445 + x = -10.641064472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.694444445' to each side of the equation. -6.694444445 + 6.694444445 + x = -10.641064472 + 6.694444445 Combine like terms: -6.694444445 + 6.694444445 = 0.000000000 0.000000000 + x = -10.641064472 + 6.694444445 x = -10.641064472 + 6.694444445 Combine like terms: -10.641064472 + 6.694444445 = -3.946620027 x = -3.946620027 Simplifying x = -3.946620027Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.335508917, -3.946620027}
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