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Simplifying 4 = -0.0055x2 + 1.15x + 10 Reorder the terms: 4 = 10 + 1.15x + -0.0055x2 Solving 4 = 10 + 1.15x + -0.0055x2 Solving for variable 'x'. Combine like terms: 4 + -10 = -6 -6 + -1.15x + 0.0055x2 = 10 + 1.15x + -0.0055x2 + -10 + -1.15x + 0.0055x2 Reorder the terms: -6 + -1.15x + 0.0055x2 = 10 + -10 + 1.15x + -1.15x + -0.0055x2 + 0.0055x2 Combine like terms: 10 + -10 = 0 -6 + -1.15x + 0.0055x2 = 0 + 1.15x + -1.15x + -0.0055x2 + 0.0055x2 -6 + -1.15x + 0.0055x2 = 1.15x + -1.15x + -0.0055x2 + 0.0055x2 Combine like terms: 1.15x + -1.15x = 0.00 -6 + -1.15x + 0.0055x2 = 0.00 + -0.0055x2 + 0.0055x2 -6 + -1.15x + 0.0055x2 = -0.0055x2 + 0.0055x2 Combine like terms: -0.0055x2 + 0.0055x2 = 0.0000 -6 + -1.15x + 0.0055x2 = 0.0000 Begin completing the square. Divide all terms by 0.0055 the coefficient of the squared term: Divide each side by '0.0055'. -1090.909091 + -209.0909091x + x2 = 0 Move the constant term to the right: Add '1090.909091' to each side of the equation. -1090.909091 + -209.0909091x + 1090.909091 + x2 = 0 + 1090.909091 Reorder the terms: -1090.909091 + 1090.909091 + -209.0909091x + x2 = 0 + 1090.909091 Combine like terms: -1090.909091 + 1090.909091 = 0.000000 0.000000 + -209.0909091x + x2 = 0 + 1090.909091 -209.0909091x + x2 = 0 + 1090.909091 Combine like terms: 0 + 1090.909091 = 1090.909091 -209.0909091x + x2 = 1090.909091 The x term is -209.0909091x. Take half its coefficient (-104.5454546). Square it (10929.75208) and add it to both sides. Add '10929.75208' to each side of the equation. -209.0909091x + 10929.75208 + x2 = 1090.909091 + 10929.75208 Reorder the terms: 10929.75208 + -209.0909091x + x2 = 1090.909091 + 10929.75208 Combine like terms: 1090.909091 + 10929.75208 = 12020.661171 10929.75208 + -209.0909091x + x2 = 12020.661171 Factor a perfect square on the left side: (x + -104.5454546)(x + -104.5454546) = 12020.661171 Calculate the square root of the right side: 109.638775855 Break this problem into two subproblems by setting (x + -104.5454546) equal to 109.638775855 and -109.638775855.Subproblem 1
x + -104.5454546 = 109.638775855 Simplifying x + -104.5454546 = 109.638775855 Reorder the terms: -104.5454546 + x = 109.638775855 Solving -104.5454546 + x = 109.638775855 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '104.5454546' to each side of the equation. -104.5454546 + 104.5454546 + x = 109.638775855 + 104.5454546 Combine like terms: -104.5454546 + 104.5454546 = 0.0000000 0.0000000 + x = 109.638775855 + 104.5454546 x = 109.638775855 + 104.5454546 Combine like terms: 109.638775855 + 104.5454546 = 214.184230455 x = 214.184230455 Simplifying x = 214.184230455Subproblem 2
x + -104.5454546 = -109.638775855 Simplifying x + -104.5454546 = -109.638775855 Reorder the terms: -104.5454546 + x = -109.638775855 Solving -104.5454546 + x = -109.638775855 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '104.5454546' to each side of the equation. -104.5454546 + 104.5454546 + x = -109.638775855 + 104.5454546 Combine like terms: -104.5454546 + 104.5454546 = 0.0000000 0.0000000 + x = -109.638775855 + 104.5454546 x = -109.638775855 + 104.5454546 Combine like terms: -109.638775855 + 104.5454546 = -5.093321255 x = -5.093321255 Simplifying x = -5.093321255Solution
The solution to the problem is based on the solutions from the subproblems. x = {214.184230455, -5.093321255}
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