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Simplifying (X * X) + -2X = 6 Multiply X * X (X2) + -2X = 6 X2 + -2X = 6 Reorder the terms: -2X + X2 = 6 Solving -2X + X2 = 6 Solving for variable 'X'. Reorder the terms: -6 + -2X + X2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + -2X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -2X + 6 + X2 = 0 + 6 Reorder the terms: -6 + 6 + -2X + X2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -2X + X2 = 0 + 6 -2X + X2 = 0 + 6 Combine like terms: 0 + 6 = 6 -2X + X2 = 6 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 = 6 + 1 Reorder the terms: 1 + -2X + X2 = 6 + 1 Combine like terms: 6 + 1 = 7 1 + -2X + X2 = 7 Factor a perfect square on the left side: (X + -1)(X + -1) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (X + -1) equal to 2.645751311 and -2.645751311.Subproblem 1
X + -1 = 2.645751311 Simplifying X + -1 = 2.645751311 Reorder the terms: -1 + X = 2.645751311 Solving -1 + X = 2.645751311 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 = 2.645751311 + 1 Combine like terms: -1 + 1 = 0 0 + X = 2.645751311 + 1 X = 2.645751311 + 1 Combine like terms: 2.645751311 + 1 = 3.645751311 X = 3.645751311 Simplifying X = 3.645751311Subproblem 2
X + -1 = -2.645751311 Simplifying X + -1 = -2.645751311 Reorder the terms: -1 + X = -2.645751311 Solving -1 + X = -2.645751311 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 = -2.645751311 + 1 Combine like terms: -1 + 1 = 0 0 + X = -2.645751311 + 1 X = -2.645751311 + 1 Combine like terms: -2.645751311 + 1 = -1.645751311 X = -1.645751311 Simplifying X = -1.645751311Solution
The solution to the problem is based on the solutions from the subproblems. X = {3.645751311, -1.645751311}
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