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Simplifying 9x2 + -37x + 31 = 0 Reorder the terms: 31 + -37x + 9x2 = 0 Solving 31 + -37x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 3.444444444 + -4.111111111x + x2 = 0 Move the constant term to the right: Add '-3.444444444' to each side of the equation. 3.444444444 + -4.111111111x + -3.444444444 + x2 = 0 + -3.444444444 Reorder the terms: 3.444444444 + -3.444444444 + -4.111111111x + x2 = 0 + -3.444444444 Combine like terms: 3.444444444 + -3.444444444 = 0.000000000 0.000000000 + -4.111111111x + x2 = 0 + -3.444444444 -4.111111111x + x2 = 0 + -3.444444444 Combine like terms: 0 + -3.444444444 = -3.444444444 -4.111111111x + x2 = -3.444444444 The x term is -4.111111111x. Take half its coefficient (-2.055555556). Square it (4.225308644) and add it to both sides. Add '4.225308644' to each side of the equation. -4.111111111x + 4.225308644 + x2 = -3.444444444 + 4.225308644 Reorder the terms: 4.225308644 + -4.111111111x + x2 = -3.444444444 + 4.225308644 Combine like terms: -3.444444444 + 4.225308644 = 0.7808642 4.225308644 + -4.111111111x + x2 = 0.7808642 Factor a perfect square on the left side: (x + -2.055555556)(x + -2.055555556) = 0.7808642 Calculate the square root of the right side: 0.883665208 Break this problem into two subproblems by setting (x + -2.055555556) equal to 0.883665208 and -0.883665208.Subproblem 1
x + -2.055555556 = 0.883665208 Simplifying x + -2.055555556 = 0.883665208 Reorder the terms: -2.055555556 + x = 0.883665208 Solving -2.055555556 + x = 0.883665208 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.055555556' to each side of the equation. -2.055555556 + 2.055555556 + x = 0.883665208 + 2.055555556 Combine like terms: -2.055555556 + 2.055555556 = 0.000000000 0.000000000 + x = 0.883665208 + 2.055555556 x = 0.883665208 + 2.055555556 Combine like terms: 0.883665208 + 2.055555556 = 2.939220764 x = 2.939220764 Simplifying x = 2.939220764Subproblem 2
x + -2.055555556 = -0.883665208 Simplifying x + -2.055555556 = -0.883665208 Reorder the terms: -2.055555556 + x = -0.883665208 Solving -2.055555556 + x = -0.883665208 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.055555556' to each side of the equation. -2.055555556 + 2.055555556 + x = -0.883665208 + 2.055555556 Combine like terms: -2.055555556 + 2.055555556 = 0.000000000 0.000000000 + x = -0.883665208 + 2.055555556 x = -0.883665208 + 2.055555556 Combine like terms: -0.883665208 + 2.055555556 = 1.171890348 x = 1.171890348 Simplifying x = 1.171890348Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.939220764, 1.171890348}
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