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Simplifying 3(X2 + -1) + -2(X2 + 2X) = 5 Reorder the terms: 3(-1 + X2) + -2(X2 + 2X) = 5 (-1 * 3 + X2 * 3) + -2(X2 + 2X) = 5 (-3 + 3X2) + -2(X2 + 2X) = 5 Reorder the terms: -3 + 3X2 + -2(2X + X2) = 5 -3 + 3X2 + (2X * -2 + X2 * -2) = 5 -3 + 3X2 + (-4X + -2X2) = 5 Reorder the terms: -3 + -4X + 3X2 + -2X2 = 5 Combine like terms: 3X2 + -2X2 = 1X2 -3 + -4X + 1X2 = 5 Solving -3 + -4X + 1X2 = 5 Solving for variable 'X'. Reorder the terms: -3 + -5 + -4X + 1X2 = 5 + -5 Combine like terms: -3 + -5 = -8 -8 + -4X + 1X2 = 5 + -5 Combine like terms: 5 + -5 = 0 -8 + -4X + 1X2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + -4X + 8 + X2 = 0 + 8 Reorder the terms: -8 + 8 + -4X + X2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -4X + X2 = 0 + 8 -4X + X2 = 0 + 8 Combine like terms: 0 + 8 = 8 -4X + X2 = 8 The X term is -4X. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4X + 4 + X2 = 8 + 4 Reorder the terms: 4 + -4X + X2 = 8 + 4 Combine like terms: 8 + 4 = 12 4 + -4X + X2 = 12 Factor a perfect square on the left side: (X + -2)(X + -2) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (X + -2) equal to 3.464101615 and -3.464101615.Subproblem 1
X + -2 = 3.464101615 Simplifying X + -2 = 3.464101615 Reorder the terms: -2 + X = 3.464101615 Solving -2 + X = 3.464101615 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + X = 3.464101615 + 2 Combine like terms: -2 + 2 = 0 0 + X = 3.464101615 + 2 X = 3.464101615 + 2 Combine like terms: 3.464101615 + 2 = 5.464101615 X = 5.464101615 Simplifying X = 5.464101615Subproblem 2
X + -2 = -3.464101615 Simplifying X + -2 = -3.464101615 Reorder the terms: -2 + X = -3.464101615 Solving -2 + X = -3.464101615 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + X = -3.464101615 + 2 Combine like terms: -2 + 2 = 0 0 + X = -3.464101615 + 2 X = -3.464101615 + 2 Combine like terms: -3.464101615 + 2 = -1.464101615 X = -1.464101615 Simplifying X = -1.464101615Solution
The solution to the problem is based on the solutions from the subproblems. X = {5.464101615, -1.464101615}
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