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Simplifying 32 + 12X + -4X2 = 0 Solving 32 + 12X + -4X2 = 0 Solving for variable 'X'. Factor out the Greatest Common Factor (GCF), '4'. 4(8 + 3X + -1X2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(8 + 3X + -1X2)' equal to zero and attempt to solve: Simplifying 8 + 3X + -1X2 = 0 Solving 8 + 3X + -1X2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -8 + -3X + X2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -3X + 8 + X2 = 0 + 8 Reorder the terms: -8 + 8 + -3X + X2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -3X + X2 = 0 + 8 -3X + X2 = 0 + 8 Combine like terms: 0 + 8 = 8 -3X + X2 = 8 The X term is -3X. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3X + 2.25 + X2 = 8 + 2.25 Reorder the terms: 2.25 + -3X + X2 = 8 + 2.25 Combine like terms: 8 + 2.25 = 10.25 2.25 + -3X + X2 = 10.25 Factor a perfect square on the left side: (X + -1.5)(X + -1.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (X + -1.5) equal to 3.201562119 and -3.201562119.Subproblem 1
X + -1.5 = 3.201562119 Simplifying X + -1.5 = 3.201562119 Reorder the terms: -1.5 + X = 3.201562119 Solving -1.5 + X = 3.201562119 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + X = 3.201562119 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + X = 3.201562119 + 1.5 X = 3.201562119 + 1.5 Combine like terms: 3.201562119 + 1.5 = 4.701562119 X = 4.701562119 Simplifying X = 4.701562119Subproblem 2
X + -1.5 = -3.201562119 Simplifying X + -1.5 = -3.201562119 Reorder the terms: -1.5 + X = -3.201562119 Solving -1.5 + X = -3.201562119 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + X = -3.201562119 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + X = -3.201562119 + 1.5 X = -3.201562119 + 1.5 Combine like terms: -3.201562119 + 1.5 = -1.701562119 X = -1.701562119 Simplifying X = -1.701562119Solution
The solution to the problem is based on the solutions from the subproblems. X = {4.701562119, -1.701562119}Solution
X = {4.701562119, -1.701562119}
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