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Simplifying X(X) + -6X + -5 = 4 Multiply X * X X2 + -6X + -5 = 4 Reorder the terms: -5 + -6X + X2 = 4 Solving -5 + -6X + X2 = 4 Solving for variable 'X'. Reorder the terms: -5 + -4 + -6X + X2 = 4 + -4 Combine like terms: -5 + -4 = -9 -9 + -6X + X2 = 4 + -4 Combine like terms: 4 + -4 = 0 -9 + -6X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -6X + 9 + X2 = 0 + 9 Reorder the terms: -9 + 9 + -6X + X2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -6X + X2 = 0 + 9 -6X + X2 = 0 + 9 Combine like terms: 0 + 9 = 9 -6X + X2 = 9 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 = 9 + 9 Reorder the terms: 9 + -6X + X2 = 9 + 9 Combine like terms: 9 + 9 = 18 9 + -6X + X2 = 18 Factor a perfect square on the left side: (X + -3)(X + -3) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (X + -3) equal to 4.242640687 and -4.242640687.Subproblem 1
X + -3 = 4.242640687 Simplifying X + -3 = 4.242640687 Reorder the terms: -3 + X = 4.242640687 Solving -3 + X = 4.242640687 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 = 4.242640687 + 3 Combine like terms: -3 + 3 = 0 0 + X = 4.242640687 + 3 X = 4.242640687 + 3 Combine like terms: 4.242640687 + 3 = 7.242640687 X = 7.242640687 Simplifying X = 7.242640687Subproblem 2
X + -3 = -4.242640687 Simplifying X + -3 = -4.242640687 Reorder the terms: -3 + X = -4.242640687 Solving -3 + X = -4.242640687 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 = -4.242640687 + 3 Combine like terms: -3 + 3 = 0 0 + X = -4.242640687 + 3 X = -4.242640687 + 3 Combine like terms: -4.242640687 + 3 = -1.242640687 X = -1.242640687 Simplifying X = -1.242640687Solution
The solution to the problem is based on the solutions from the subproblems. X = {7.242640687, -1.242640687}
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