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Simplifying 36x2 + -476x + -2463 = 0 Reorder the terms: -2463 + -476x + 36x2 = 0 Solving -2463 + -476x + 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 + -13.22222222x + x2 = 0 Move the constant term to the right: Add '68.41666667' to each side of the equation. -68.41666667 + -13.22222222x + 68.41666667 + x2 = 0 + 68.41666667 Reorder the terms: -68.41666667 + 68.41666667 + -13.22222222x + x2 = 0 + 68.41666667 Combine like terms: -68.41666667 + 68.41666667 = 0.00000000 0.00000000 + -13.22222222x + x2 = 0 + 68.41666667 -13.22222222x + x2 = 0 + 68.41666667 Combine like terms: 0 + 68.41666667 = 68.41666667 -13.22222222x + x2 = 68.41666667 The x term is -13.22222222x. Take half its coefficient (-6.61111111). Square it (43.70679011) and add it to both sides. Add '43.70679011' to each side of the equation. -13.22222222x + 43.70679011 + x2 = 68.41666667 + 43.70679011 Reorder the terms: 43.70679011 + -13.22222222x + x2 = 68.41666667 + 43.70679011 Combine like terms: 68.41666667 + 43.70679011 = 112.12345678 43.70679011 + -13.22222222x + x2 = 112.12345678 Factor a perfect square on the left side: (x + -6.61111111)(x + -6.61111111) = 112.12345678 Calculate the square root of the right side: 10.588836422 Break this problem into two subproblems by setting (x + -6.61111111) equal to 10.588836422 and -10.588836422.Subproblem 1
x + -6.61111111 = 10.588836422 Simplifying x + -6.61111111 = 10.588836422 Reorder the terms: -6.61111111 + x = 10.588836422 Solving -6.61111111 + x = 10.588836422 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.61111111' to each side of the equation. -6.61111111 + 6.61111111 + x = 10.588836422 + 6.61111111 Combine like terms: -6.61111111 + 6.61111111 = 0.00000000 0.00000000 + x = 10.588836422 + 6.61111111 x = 10.588836422 + 6.61111111 Combine like terms: 10.588836422 + 6.61111111 = 17.199947532 x = 17.199947532 Simplifying x = 17.199947532Subproblem 2
x + -6.61111111 = -10.588836422 Simplifying x + -6.61111111 = -10.588836422 Reorder the terms: -6.61111111 + x = -10.588836422 Solving -6.61111111 + x = -10.588836422 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.61111111' to each side of the equation. -6.61111111 + 6.61111111 + x = -10.588836422 + 6.61111111 Combine like terms: -6.61111111 + 6.61111111 = 0.00000000 0.00000000 + x = -10.588836422 + 6.61111111 x = -10.588836422 + 6.61111111 Combine like terms: -10.588836422 + 6.61111111 = -3.977725312 x = -3.977725312 Simplifying x = -3.977725312Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.199947532, -3.977725312}
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