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Simplifying 36x2 + -476x + -2464 = 0 Reorder the terms: -2464 + -476x + 36x2 = 0 Solving -2464 + -476x + 36x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-616 + -119x + 9x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-616 + -119x + 9x2)' equal to zero and attempt to solve: Simplifying -616 + -119x + 9x2 = 0 Solving -616 + -119x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -68.44444444 + -13.22222222x + x2 = 0 Move the constant term to the right: Add '68.44444444' to each side of the equation. -68.44444444 + -13.22222222x + 68.44444444 + x2 = 0 + 68.44444444 Reorder the terms: -68.44444444 + 68.44444444 + -13.22222222x + x2 = 0 + 68.44444444 Combine like terms: -68.44444444 + 68.44444444 = 0.00000000 0.00000000 + -13.22222222x + x2 = 0 + 68.44444444 -13.22222222x + x2 = 0 + 68.44444444 Combine like terms: 0 + 68.44444444 = 68.44444444 -13.22222222x + x2 = 68.44444444 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 = 68.44444444 + 43.70679011 Reorder the terms: 43.70679011 + -13.22222222x + x2 = 68.44444444 + 43.70679011 Combine like terms: 68.44444444 + 43.70679011 = 112.15123455 43.70679011 + -13.22222222x + x2 = 112.15123455 Factor a perfect square on the left side: (x + -6.61111111)(x + -6.61111111) = 112.15123455 Calculate the square root of the right side: 10.590147995 Break this problem into two subproblems by setting (x + -6.61111111) equal to 10.590147995 and -10.590147995.Subproblem 1
x + -6.61111111 = 10.590147995 Simplifying x + -6.61111111 = 10.590147995 Reorder the terms: -6.61111111 + x = 10.590147995 Solving -6.61111111 + x = 10.590147995 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 = 10.590147995 + 6.61111111 Combine like terms: -6.61111111 + 6.61111111 = 0.00000000 0.00000000 + x = 10.590147995 + 6.61111111 x = 10.590147995 + 6.61111111 Combine like terms: 10.590147995 + 6.61111111 = 17.201259105 x = 17.201259105 Simplifying x = 17.201259105Subproblem 2
x + -6.61111111 = -10.590147995 Simplifying x + -6.61111111 = -10.590147995 Reorder the terms: -6.61111111 + x = -10.590147995 Solving -6.61111111 + x = -10.590147995 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 = -10.590147995 + 6.61111111 Combine like terms: -6.61111111 + 6.61111111 = 0.00000000 0.00000000 + x = -10.590147995 + 6.61111111 x = -10.590147995 + 6.61111111 Combine like terms: -10.590147995 + 6.61111111 = -3.979036885 x = -3.979036885 Simplifying x = -3.979036885Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.201259105, -3.979036885}Solution
x = {17.201259105, -3.979036885}
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