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Simplifying 2x2y2 + -24xy2 + 32y2 + -2y2 = 0 Reorder the terms: -24xy2 + 2x2y2 + 32y2 + -2y2 = 0 Combine like terms: 32y2 + -2y2 = 30y2 -24xy2 + 2x2y2 + 30y2 = 0 Solving -24xy2 + 2x2y2 + 30y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2y2'. 2y2(-12x + x2 + 15) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'y2' equal to zero and attempt to solve: Simplifying y2 = 0 Solving y2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y2' to each side of the equation. y2 + -1y2 = 0 + -1y2 Remove the zero: 0 = -1y2 Simplifying 0 = -1y2 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 '(-12x + x2 + 15)' equal to zero and attempt to solve: Simplifying -12x + x2 + 15 = 0 Reorder the terms: 15 + -12x + x2 = 0 Solving 15 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + -12x + -15 + x2 = 0 + -15 Reorder the terms: 15 + -15 + -12x + x2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -12x + x2 = 0 + -15 -12x + x2 = 0 + -15 Combine like terms: 0 + -15 = -15 -12x + x2 = -15 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = -15 + 36 Reorder the terms: 36 + -12x + x2 = -15 + 36 Combine like terms: -15 + 36 = 21 36 + -12x + x2 = 21 Factor a perfect square on the left side: (x + -6)(x + -6) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (x + -6) equal to 4.582575695 and -4.582575695.Subproblem 1
x + -6 = 4.582575695 Simplifying x + -6 = 4.582575695 Reorder the terms: -6 + x = 4.582575695 Solving -6 + x = 4.582575695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 4.582575695 + 6 Combine like terms: -6 + 6 = 0 0 + x = 4.582575695 + 6 x = 4.582575695 + 6 Combine like terms: 4.582575695 + 6 = 10.582575695 x = 10.582575695 Simplifying x = 10.582575695Subproblem 2
x + -6 = -4.582575695 Simplifying x + -6 = -4.582575695 Reorder the terms: -6 + x = -4.582575695 Solving -6 + x = -4.582575695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -4.582575695 + 6 Combine like terms: -6 + 6 = 0 0 + x = -4.582575695 + 6 x = -4.582575695 + 6 Combine like terms: -4.582575695 + 6 = 1.417424305 x = 1.417424305 Simplifying x = 1.417424305Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.582575695, 1.417424305}Solution
x = {10.582575695, 1.417424305}
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