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Simplifying X3 + -5X = 2X2 + 7X Reorder the terms: -5X + X3 = 2X2 + 7X Reorder the terms: -5X + X3 = 7X + 2X2 Solving -5X + X3 = 7X + 2X2 Solving for variable 'X'. Reorder the terms: -5X + -7X + -2X2 + X3 = 7X + 2X2 + -7X + -2X2 Combine like terms: -5X + -7X = -12X -12X + -2X2 + X3 = 7X + 2X2 + -7X + -2X2 Reorder the terms: -12X + -2X2 + X3 = 7X + -7X + 2X2 + -2X2 Combine like terms: 7X + -7X = 0 -12X + -2X2 + X3 = 0 + 2X2 + -2X2 -12X + -2X2 + X3 = 2X2 + -2X2 Combine like terms: 2X2 + -2X2 = 0 -12X + -2X2 + X3 = 0 Factor out the Greatest Common Factor (GCF), 'X'. X(-12 + -2X + X2) = 0Subproblem 1
Set the factor 'X' equal to zero and attempt to solve: Simplifying X = 0 Solving X = 0 Move all terms containing X to the left, all other terms to the right. Simplifying X = 0Subproblem 2
Set the factor '(-12 + -2X + X2)' equal to zero and attempt to solve: Simplifying -12 + -2X + X2 = 0 Solving -12 + -2X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + -2X + 12 + X2 = 0 + 12 Reorder the terms: -12 + 12 + -2X + X2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -2X + X2 = 0 + 12 -2X + X2 = 0 + 12 Combine like terms: 0 + 12 = 12 -2X + X2 = 12 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 = 12 + 1 Reorder the terms: 1 + -2X + X2 = 12 + 1 Combine like terms: 12 + 1 = 13 1 + -2X + X2 = 13 Factor a perfect square on the left side: (X + -1)(X + -1) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (X + -1) equal to 3.605551275 and -3.605551275.Subproblem 1
X + -1 = 3.605551275 Simplifying X + -1 = 3.605551275 Reorder the terms: -1 + X = 3.605551275 Solving -1 + X = 3.605551275 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 = 3.605551275 + 1 Combine like terms: -1 + 1 = 0 0 + X = 3.605551275 + 1 X = 3.605551275 + 1 Combine like terms: 3.605551275 + 1 = 4.605551275 X = 4.605551275 Simplifying X = 4.605551275Subproblem 2
X + -1 = -3.605551275 Simplifying X + -1 = -3.605551275 Reorder the terms: -1 + X = -3.605551275 Solving -1 + X = -3.605551275 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 = -3.605551275 + 1 Combine like terms: -1 + 1 = 0 0 + X = -3.605551275 + 1 X = -3.605551275 + 1 Combine like terms: -3.605551275 + 1 = -2.605551275 X = -2.605551275 Simplifying X = -2.605551275Solution
The solution to the problem is based on the solutions from the subproblems. X = {4.605551275, -2.605551275}Solution
X = {0, 4.605551275, -2.605551275}
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