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Simplifying 2X2 + -8X = 80 Reorder the terms: -8X + 2X2 = 80 Solving -8X + 2X2 = 80 Solving for variable 'X'. Reorder the terms: -80 + -8X + 2X2 = 80 + -80 Combine like terms: 80 + -80 = 0 -80 + -8X + 2X2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-40 + -4X + X2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-40 + -4X + X2)' equal to zero and attempt to solve: Simplifying -40 + -4X + X2 = 0 Solving -40 + -4X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '40' to each side of the equation. -40 + -4X + 40 + X2 = 0 + 40 Reorder the terms: -40 + 40 + -4X + X2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -4X + X2 = 0 + 40 -4X + X2 = 0 + 40 Combine like terms: 0 + 40 = 40 -4X + X2 = 40 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 = 40 + 4 Reorder the terms: 4 + -4X + X2 = 40 + 4 Combine like terms: 40 + 4 = 44 4 + -4X + X2 = 44 Factor a perfect square on the left side: (X + -2)(X + -2) = 44 Calculate the square root of the right side: 6.633249581 Break this problem into two subproblems by setting (X + -2) equal to 6.633249581 and -6.633249581.Subproblem 1
X + -2 = 6.633249581 Simplifying X + -2 = 6.633249581 Reorder the terms: -2 + X = 6.633249581 Solving -2 + X = 6.633249581 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 = 6.633249581 + 2 Combine like terms: -2 + 2 = 0 0 + X = 6.633249581 + 2 X = 6.633249581 + 2 Combine like terms: 6.633249581 + 2 = 8.633249581 X = 8.633249581 Simplifying X = 8.633249581Subproblem 2
X + -2 = -6.633249581 Simplifying X + -2 = -6.633249581 Reorder the terms: -2 + X = -6.633249581 Solving -2 + X = -6.633249581 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 = -6.633249581 + 2 Combine like terms: -2 + 2 = 0 0 + X = -6.633249581 + 2 X = -6.633249581 + 2 Combine like terms: -6.633249581 + 2 = -4.633249581 X = -4.633249581 Simplifying X = -4.633249581Solution
The solution to the problem is based on the solutions from the subproblems. X = {8.633249581, -4.633249581}Solution
X = {8.633249581, -4.633249581}
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