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Simplifying x2 + -6x + -31 = 2 Reorder the terms: -31 + -6x + x2 = 2 Solving -31 + -6x + x2 = 2 Solving for variable 'x'. Reorder the terms: -31 + -2 + -6x + x2 = 2 + -2 Combine like terms: -31 + -2 = -33 -33 + -6x + x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -33 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '33' to each side of the equation. -33 + -6x + 33 + x2 = 0 + 33 Reorder the terms: -33 + 33 + -6x + x2 = 0 + 33 Combine like terms: -33 + 33 = 0 0 + -6x + x2 = 0 + 33 -6x + x2 = 0 + 33 Combine like terms: 0 + 33 = 33 -6x + x2 = 33 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 33 + 9 Reorder the terms: 9 + -6x + x2 = 33 + 9 Combine like terms: 33 + 9 = 42 9 + -6x + x2 = 42 Factor a perfect square on the left side: (x + -3)(x + -3) = 42 Calculate the square root of the right side: 6.480740698 Break this problem into two subproblems by setting (x + -3) equal to 6.480740698 and -6.480740698.Subproblem 1
x + -3 = 6.480740698 Simplifying x + -3 = 6.480740698 Reorder the terms: -3 + x = 6.480740698 Solving -3 + x = 6.480740698 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 6.480740698 + 3 Combine like terms: -3 + 3 = 0 0 + x = 6.480740698 + 3 x = 6.480740698 + 3 Combine like terms: 6.480740698 + 3 = 9.480740698 x = 9.480740698 Simplifying x = 9.480740698Subproblem 2
x + -3 = -6.480740698 Simplifying x + -3 = -6.480740698 Reorder the terms: -3 + x = -6.480740698 Solving -3 + x = -6.480740698 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -6.480740698 + 3 Combine like terms: -3 + 3 = 0 0 + x = -6.480740698 + 3 x = -6.480740698 + 3 Combine like terms: -6.480740698 + 3 = -3.480740698 x = -3.480740698 Simplifying x = -3.480740698Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.480740698, -3.480740698}
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