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Simplifying 110 = (0.0225x2) + -6x + 400 Reorder the terms: 110 = 400 + -6x + (0.0225x2) Solving 110 = 400 + -6x + (0.0225x2) Solving for variable 'x'. Combine like terms: 110 + -400 = -290 -290 + 6x + (-0.0225x2) = 400 + -6x + (0.0225x2) + -400 + 6x + (-0.0225x2) Reorder the terms: -290 + 6x + (-0.0225x2) = 400 + -400 + -6x + 6x + (0.0225x2) + (-0.0225x2) Combine like terms: 400 + -400 = 0 -290 + 6x + (-0.0225x2) = 0 + -6x + 6x + (0.0225x2) + (-0.0225x2) -290 + 6x + (-0.0225x2) = -6x + 6x + (0.0225x2) + (-0.0225x2) Combine like terms: -6x + 6x = 0 -290 + 6x + (-0.0225x2) = 0 + (0.0225x2) + (-0.0225x2) -290 + 6x + (-0.0225x2) = (0.0225x2) + (-0.0225x2) Combine like terms: (0.0225x2) + (-0.0225x2) = 0.0000 -290 + 6x + (-0.0225x2) = 0.0000 Begin completing the square. Divide all terms by -0.0225 the coefficient of the squared term: Divide each side by '-0.0225'. 12888.88889 + -266.6666667x + x2 = 0 Move the constant term to the right: Add '-12888.88889' to each side of the equation. 12888.88889 + -266.6666667x + -12888.88889 + x2 = 0 + -12888.88889 Reorder the terms: 12888.88889 + -12888.88889 + -266.6666667x + x2 = 0 + -12888.88889 Combine like terms: 12888.88889 + -12888.88889 = 0.00000 0.00000 + -266.6666667x + x2 = 0 + -12888.88889 -266.6666667x + x2 = 0 + -12888.88889 Combine like terms: 0 + -12888.88889 = -12888.88889 -266.6666667x + x2 = -12888.88889 The x term is -266.6666667x. Take half its coefficient (-133.3333334). Square it (17777.77780) and add it to both sides. Add '17777.77780' to each side of the equation. -266.6666667x + 17777.77780 + x2 = -12888.88889 + 17777.77780 Reorder the terms: 17777.77780 + -266.6666667x + x2 = -12888.88889 + 17777.77780 Combine like terms: -12888.88889 + 17777.77780 = 4888.88891 17777.77780 + -266.6666667x + x2 = 4888.88891 Factor a perfect square on the left side: ((x) + -133.3333334)((x) + -133.3333334) = 4888.88891 Calculate the square root of the right side: 69.920590029 Break this problem into two subproblems by setting ((x) + -133.3333334) equal to 69.920590029 and -69.920590029.Subproblem 1
(x) + -133.3333334 = 69.920590029 Simplifying (x) + -133.3333334 = 69.920590029 x + -133.3333334 = 69.920590029 Reorder the terms: -133.3333334 + x = 69.920590029 Solving -133.3333334 + x = 69.920590029 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '133.3333334' to each side of the equation. -133.3333334 + 133.3333334 + x = 69.920590029 + 133.3333334 Combine like terms: -133.3333334 + 133.3333334 = 0.0000000 0.0000000 + x = 69.920590029 + 133.3333334 x = 69.920590029 + 133.3333334 Combine like terms: 69.920590029 + 133.3333334 = 203.253923429 x = 203.253923429 Simplifying x = 203.253923429Subproblem 2
(x) + -133.3333334 = -69.920590029 Simplifying (x) + -133.3333334 = -69.920590029 x + -133.3333334 = -69.920590029 Reorder the terms: -133.3333334 + x = -69.920590029 Solving -133.3333334 + x = -69.920590029 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '133.3333334' to each side of the equation. -133.3333334 + 133.3333334 + x = -69.920590029 + 133.3333334 Combine like terms: -133.3333334 + 133.3333334 = 0.0000000 0.0000000 + x = -69.920590029 + 133.3333334 x = -69.920590029 + 133.3333334 Combine like terms: -69.920590029 + 133.3333334 = 63.412743371 x = 63.412743371 Simplifying x = 63.412743371Solution
The solution to the problem is based on the solutions from the subproblems. x = {203.253923429, 63.412743371}
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