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Simplifying 2.232x2 + -4.114x = 6.219 Reorder the terms: -4.114x + 2.232x2 = 6.219 Solving -4.114x + 2.232x2 = 6.219 Solving for variable 'x'. Reorder the terms: -6.219 + -4.114x + 2.232x2 = 6.219 + -6.219 Combine like terms: 6.219 + -6.219 = 0.000 -6.219 + -4.114x + 2.232x2 = 0.000 Begin completing the square. Divide all terms by 2.232 the coefficient of the squared term: Divide each side by '2.232'. -2.786290323 + -1.843189964x + x2 = 0 Move the constant term to the right: Add '2.786290323' to each side of the equation. -2.786290323 + -1.843189964x + 2.786290323 + x2 = 0 + 2.786290323 Reorder the terms: -2.786290323 + 2.786290323 + -1.843189964x + x2 = 0 + 2.786290323 Combine like terms: -2.786290323 + 2.786290323 = 0.000000000 0.000000000 + -1.843189964x + x2 = 0 + 2.786290323 -1.843189964x + x2 = 0 + 2.786290323 Combine like terms: 0 + 2.786290323 = 2.786290323 -1.843189964x + x2 = 2.786290323 The x term is -1.843189964x. Take half its coefficient (-0.921594982). Square it (0.8493373108) and add it to both sides. Add '0.8493373108' to each side of the equation. -1.843189964x + 0.8493373108 + x2 = 2.786290323 + 0.8493373108 Reorder the terms: 0.8493373108 + -1.843189964x + x2 = 2.786290323 + 0.8493373108 Combine like terms: 2.786290323 + 0.8493373108 = 3.6356276338 0.8493373108 + -1.843189964x + x2 = 3.6356276338 Factor a perfect square on the left side: (x + -0.921594982)(x + -0.921594982) = 3.6356276338 Calculate the square root of the right side: 1.906732187 Break this problem into two subproblems by setting (x + -0.921594982) equal to 1.906732187 and -1.906732187.Subproblem 1
x + -0.921594982 = 1.906732187 Simplifying x + -0.921594982 = 1.906732187 Reorder the terms: -0.921594982 + x = 1.906732187 Solving -0.921594982 + x = 1.906732187 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.921594982' to each side of the equation. -0.921594982 + 0.921594982 + x = 1.906732187 + 0.921594982 Combine like terms: -0.921594982 + 0.921594982 = 0.000000000 0.000000000 + x = 1.906732187 + 0.921594982 x = 1.906732187 + 0.921594982 Combine like terms: 1.906732187 + 0.921594982 = 2.828327169 x = 2.828327169 Simplifying x = 2.828327169Subproblem 2
x + -0.921594982 = -1.906732187 Simplifying x + -0.921594982 = -1.906732187 Reorder the terms: -0.921594982 + x = -1.906732187 Solving -0.921594982 + x = -1.906732187 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.921594982' to each side of the equation. -0.921594982 + 0.921594982 + x = -1.906732187 + 0.921594982 Combine like terms: -0.921594982 + 0.921594982 = 0.000000000 0.000000000 + x = -1.906732187 + 0.921594982 x = -1.906732187 + 0.921594982 Combine like terms: -1.906732187 + 0.921594982 = -0.985137205 x = -0.985137205 Simplifying x = -0.985137205Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.828327169, -0.985137205}
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