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Simplifying X * X + -2X + 1 = 40 Multiply X * X X2 + -2X + 1 = 40 Reorder the terms: 1 + -2X + X2 = 40 Solving 1 + -2X + X2 = 40 Solving for variable 'X'. Reorder the terms: 1 + -40 + -2X + X2 = 40 + -40 Combine like terms: 1 + -40 = -39 -39 + -2X + X2 = 40 + -40 Combine like terms: 40 + -40 = 0 -39 + -2X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '39' to each side of the equation. -39 + -2X + 39 + X2 = 0 + 39 Reorder the terms: -39 + 39 + -2X + X2 = 0 + 39 Combine like terms: -39 + 39 = 0 0 + -2X + X2 = 0 + 39 -2X + X2 = 0 + 39 Combine like terms: 0 + 39 = 39 -2X + X2 = 39 The X term is -2X. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2X + 1 + X2 = 39 + 1 Reorder the terms: 1 + -2X + X2 = 39 + 1 Combine like terms: 39 + 1 = 40 1 + -2X + X2 = 40 Factor a perfect square on the left side: (X + -1)(X + -1) = 40 Calculate the square root of the right side: 6.32455532 Break this problem into two subproblems by setting (X + -1) equal to 6.32455532 and -6.32455532.Subproblem 1
X + -1 = 6.32455532 Simplifying X + -1 = 6.32455532 Reorder the terms: -1 + X = 6.32455532 Solving -1 + X = 6.32455532 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + X = 6.32455532 + 1 Combine like terms: -1 + 1 = 0 0 + X = 6.32455532 + 1 X = 6.32455532 + 1 Combine like terms: 6.32455532 + 1 = 7.32455532 X = 7.32455532 Simplifying X = 7.32455532Subproblem 2
X + -1 = -6.32455532 Simplifying X + -1 = -6.32455532 Reorder the terms: -1 + X = -6.32455532 Solving -1 + X = -6.32455532 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + X = -6.32455532 + 1 Combine like terms: -1 + 1 = 0 0 + X = -6.32455532 + 1 X = -6.32455532 + 1 Combine like terms: -6.32455532 + 1 = -5.32455532 X = -5.32455532 Simplifying X = -5.32455532Solution
The solution to the problem is based on the solutions from the subproblems. X = {7.32455532, -5.32455532}
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