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Simplifying 14500 = -88x2 + 17108x + -813360 Reorder the terms: 14500 = -813360 + 17108x + -88x2 Solving 14500 = -813360 + 17108x + -88x2 Solving for variable 'x'. Combine like terms: 14500 + 813360 = 827860 827860 + -17108x + 88x2 = -813360 + 17108x + -88x2 + 813360 + -17108x + 88x2 Reorder the terms: 827860 + -17108x + 88x2 = -813360 + 813360 + 17108x + -17108x + -88x2 + 88x2 Combine like terms: -813360 + 813360 = 0 827860 + -17108x + 88x2 = 0 + 17108x + -17108x + -88x2 + 88x2 827860 + -17108x + 88x2 = 17108x + -17108x + -88x2 + 88x2 Combine like terms: 17108x + -17108x = 0 827860 + -17108x + 88x2 = 0 + -88x2 + 88x2 827860 + -17108x + 88x2 = -88x2 + 88x2 Combine like terms: -88x2 + 88x2 = 0 827860 + -17108x + 88x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(206965 + -4277x + 22x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(206965 + -4277x + 22x2)' equal to zero and attempt to solve: Simplifying 206965 + -4277x + 22x2 = 0 Solving 206965 + -4277x + 22x2 = 0 Begin completing the square. Divide all terms by 22 the coefficient of the squared term: Divide each side by '22'. 9407.5 + -194.4090909x + x2 = 0 Move the constant term to the right: Add '-9407.5' to each side of the equation. 9407.5 + -194.4090909x + -9407.5 + x2 = 0 + -9407.5 Reorder the terms: 9407.5 + -9407.5 + -194.4090909x + x2 = 0 + -9407.5 Combine like terms: 9407.5 + -9407.5 = 0.0 0.0 + -194.4090909x + x2 = 0 + -9407.5 -194.4090909x + x2 = 0 + -9407.5 Combine like terms: 0 + -9407.5 = -9407.5 -194.4090909x + x2 = -9407.5 The x term is -194.4090909x. Take half its coefficient (-97.20454545). Square it (9448.723656) and add it to both sides. Add '9448.723656' to each side of the equation. -194.4090909x + 9448.723656 + x2 = -9407.5 + 9448.723656 Reorder the terms: 9448.723656 + -194.4090909x + x2 = -9407.5 + 9448.723656 Combine like terms: -9407.5 + 9448.723656 = 41.223656 9448.723656 + -194.4090909x + x2 = 41.223656 Factor a perfect square on the left side: (x + -97.20454545)(x + -97.20454545) = 41.223656 Calculate the square root of the right side: 6.420565084 Break this problem into two subproblems by setting (x + -97.20454545) equal to 6.420565084 and -6.420565084.Subproblem 1
x + -97.20454545 = 6.420565084 Simplifying x + -97.20454545 = 6.420565084 Reorder the terms: -97.20454545 + x = 6.420565084 Solving -97.20454545 + x = 6.420565084 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '97.20454545' to each side of the equation. -97.20454545 + 97.20454545 + x = 6.420565084 + 97.20454545 Combine like terms: -97.20454545 + 97.20454545 = 0.00000000 0.00000000 + x = 6.420565084 + 97.20454545 x = 6.420565084 + 97.20454545 Combine like terms: 6.420565084 + 97.20454545 = 103.625110534 x = 103.625110534 Simplifying x = 103.625110534Subproblem 2
x + -97.20454545 = -6.420565084 Simplifying x + -97.20454545 = -6.420565084 Reorder the terms: -97.20454545 + x = -6.420565084 Solving -97.20454545 + x = -6.420565084 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '97.20454545' to each side of the equation. -97.20454545 + 97.20454545 + x = -6.420565084 + 97.20454545 Combine like terms: -97.20454545 + 97.20454545 = 0.00000000 0.00000000 + x = -6.420565084 + 97.20454545 x = -6.420565084 + 97.20454545 Combine like terms: -6.420565084 + 97.20454545 = 90.783980366 x = 90.783980366 Simplifying x = 90.783980366Solution
The solution to the problem is based on the solutions from the subproblems. x = {103.625110534, 90.783980366}Solution
x = {103.625110534, 90.783980366}
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