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Simplifying 100 + 36X + -4X2 = 80 + 12X Solving 100 + 36X + -4X2 = 80 + 12X Solving for variable 'X'. Reorder the terms: 100 + -80 + 36X + -12X + -4X2 = 80 + 12X + -80 + -12X Combine like terms: 100 + -80 = 20 20 + 36X + -12X + -4X2 = 80 + 12X + -80 + -12X Combine like terms: 36X + -12X = 24X 20 + 24X + -4X2 = 80 + 12X + -80 + -12X Reorder the terms: 20 + 24X + -4X2 = 80 + -80 + 12X + -12X Combine like terms: 80 + -80 = 0 20 + 24X + -4X2 = 0 + 12X + -12X 20 + 24X + -4X2 = 12X + -12X Combine like terms: 12X + -12X = 0 20 + 24X + -4X2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(5 + 6X + -1X2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(5 + 6X + -1X2)' equal to zero and attempt to solve: Simplifying 5 + 6X + -1X2 = 0 Solving 5 + 6X + -1X2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -5 + -6X + X2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -6X + 5 + X2 = 0 + 5 Reorder the terms: -5 + 5 + -6X + X2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -6X + X2 = 0 + 5 -6X + X2 = 0 + 5 Combine like terms: 0 + 5 = 5 -6X + X2 = 5 The X term is -6X. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6X + 9 + X2 = 5 + 9 Reorder the terms: 9 + -6X + X2 = 5 + 9 Combine like terms: 5 + 9 = 14 9 + -6X + X2 = 14 Factor a perfect square on the left side: (X + -3)(X + -3) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (X + -3) equal to 3.741657387 and -3.741657387.Subproblem 1
X + -3 = 3.741657387 Simplifying X + -3 = 3.741657387 Reorder the terms: -3 + X = 3.741657387 Solving -3 + X = 3.741657387 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + X = 3.741657387 + 3 Combine like terms: -3 + 3 = 0 0 + X = 3.741657387 + 3 X = 3.741657387 + 3 Combine like terms: 3.741657387 + 3 = 6.741657387 X = 6.741657387 Simplifying X = 6.741657387Subproblem 2
X + -3 = -3.741657387 Simplifying X + -3 = -3.741657387 Reorder the terms: -3 + X = -3.741657387 Solving -3 + X = -3.741657387 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + X = -3.741657387 + 3 Combine like terms: -3 + 3 = 0 0 + X = -3.741657387 + 3 X = -3.741657387 + 3 Combine like terms: -3.741657387 + 3 = -0.741657387 X = -0.741657387 Simplifying X = -0.741657387Solution
The solution to the problem is based on the solutions from the subproblems. X = {6.741657387, -0.741657387}Solution
X = {6.741657387, -0.741657387}
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