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Simplifying 2x2y + 4xy + -24y = 0 Reorder the terms: 4xy + 2x2y + -24y = 0 Solving 4xy + 2x2y + -24y = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2y'. 2y(2x + x2 + -12) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'y' equal to zero and attempt to solve: Simplifying y = 0 Solving y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. y + -1y = 0 + -1y Remove the zero: 0 = -1y Simplifying 0 = -1y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(2x + x2 + -12)' equal to zero and attempt to solve: Simplifying 2x + x2 + -12 = 0 Reorder the terms: -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 = 2.605551275 x = 2.605551275 Simplifying x = 2.605551275Subproblem 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 = -4.605551275 x = -4.605551275 Simplifying x = -4.605551275Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.605551275, -4.605551275}Solution
x = {2.605551275, -4.605551275}
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