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Simplifying 0 = -2.2x2 + 5.3x + 4 Reorder the terms: 0 = 4 + 5.3x + -2.2x2 Solving 0 = 4 + 5.3x + -2.2x2 Solving for variable 'x'. Combine like terms: 0 + -4 = -4 -4 + -5.3x + 2.2x2 = 4 + 5.3x + -2.2x2 + -4 + -5.3x + 2.2x2 Reorder the terms: -4 + -5.3x + 2.2x2 = 4 + -4 + 5.3x + -5.3x + -2.2x2 + 2.2x2 Combine like terms: 4 + -4 = 0 -4 + -5.3x + 2.2x2 = 0 + 5.3x + -5.3x + -2.2x2 + 2.2x2 -4 + -5.3x + 2.2x2 = 5.3x + -5.3x + -2.2x2 + 2.2x2 Combine like terms: 5.3x + -5.3x = 0.0 -4 + -5.3x + 2.2x2 = 0.0 + -2.2x2 + 2.2x2 -4 + -5.3x + 2.2x2 = -2.2x2 + 2.2x2 Combine like terms: -2.2x2 + 2.2x2 = 0.0 -4 + -5.3x + 2.2x2 = 0.0 Begin completing the square. Divide all terms by 2.2 the coefficient of the squared term: Divide each side by '2.2'. -1.818181818 + -2.409090909x + x2 = 0 Move the constant term to the right: Add '1.818181818' to each side of the equation. -1.818181818 + -2.409090909x + 1.818181818 + x2 = 0 + 1.818181818 Reorder the terms: -1.818181818 + 1.818181818 + -2.409090909x + x2 = 0 + 1.818181818 Combine like terms: -1.818181818 + 1.818181818 = 0.000000000 0.000000000 + -2.409090909x + x2 = 0 + 1.818181818 -2.409090909x + x2 = 0 + 1.818181818 Combine like terms: 0 + 1.818181818 = 1.818181818 -2.409090909x + x2 = 1.818181818 The x term is -2.409090909x. Take half its coefficient (-1.204545455). Square it (1.450929753) and add it to both sides. Add '1.450929753' to each side of the equation. -2.409090909x + 1.450929753 + x2 = 1.818181818 + 1.450929753 Reorder the terms: 1.450929753 + -2.409090909x + x2 = 1.818181818 + 1.450929753 Combine like terms: 1.818181818 + 1.450929753 = 3.269111571 1.450929753 + -2.409090909x + x2 = 3.269111571 Factor a perfect square on the left side: (x + -1.204545455)(x + -1.204545455) = 3.269111571 Calculate the square root of the right side: 1.808068464 Break this problem into two subproblems by setting (x + -1.204545455) equal to 1.808068464 and -1.808068464.Subproblem 1
x + -1.204545455 = 1.808068464 Simplifying x + -1.204545455 = 1.808068464 Reorder the terms: -1.204545455 + x = 1.808068464 Solving -1.204545455 + x = 1.808068464 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.204545455' to each side of the equation. -1.204545455 + 1.204545455 + x = 1.808068464 + 1.204545455 Combine like terms: -1.204545455 + 1.204545455 = 0.000000000 0.000000000 + x = 1.808068464 + 1.204545455 x = 1.808068464 + 1.204545455 Combine like terms: 1.808068464 + 1.204545455 = 3.012613919 x = 3.012613919 Simplifying x = 3.012613919Subproblem 2
x + -1.204545455 = -1.808068464 Simplifying x + -1.204545455 = -1.808068464 Reorder the terms: -1.204545455 + x = -1.808068464 Solving -1.204545455 + x = -1.808068464 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.204545455' to each side of the equation. -1.204545455 + 1.204545455 + x = -1.808068464 + 1.204545455 Combine like terms: -1.204545455 + 1.204545455 = 0.000000000 0.000000000 + x = -1.808068464 + 1.204545455 x = -1.808068464 + 1.204545455 Combine like terms: -1.808068464 + 1.204545455 = -0.603523009 x = -0.603523009 Simplifying x = -0.603523009Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.012613919, -0.603523009}
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