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Simplifying 160 = 4X2 + 38X + 112 Reorder the terms: 160 = 112 + 38X + 4X2 Solving 160 = 112 + 38X + 4X2 Solving for variable 'X'. Combine like terms: 160 + -112 = 48 48 + -38X + -4X2 = 112 + 38X + 4X2 + -112 + -38X + -4X2 Reorder the terms: 48 + -38X + -4X2 = 112 + -112 + 38X + -38X + 4X2 + -4X2 Combine like terms: 112 + -112 = 0 48 + -38X + -4X2 = 0 + 38X + -38X + 4X2 + -4X2 48 + -38X + -4X2 = 38X + -38X + 4X2 + -4X2 Combine like terms: 38X + -38X = 0 48 + -38X + -4X2 = 0 + 4X2 + -4X2 48 + -38X + -4X2 = 4X2 + -4X2 Combine like terms: 4X2 + -4X2 = 0 48 + -38X + -4X2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(24 + -19X + -2X2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(24 + -19X + -2X2)' equal to zero and attempt to solve: Simplifying 24 + -19X + -2X2 = 0 Solving 24 + -19X + -2X2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -12 + 9.5X + X2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + 9.5X + 12 + X2 = 0 + 12 Reorder the terms: -12 + 12 + 9.5X + X2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 9.5X + X2 = 0 + 12 9.5X + X2 = 0 + 12 Combine like terms: 0 + 12 = 12 9.5X + X2 = 12 The X term is 9.5X. Take half its coefficient (4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. 9.5X + 22.5625 + X2 = 12 + 22.5625 Reorder the terms: 22.5625 + 9.5X + X2 = 12 + 22.5625 Combine like terms: 12 + 22.5625 = 34.5625 22.5625 + 9.5X + X2 = 34.5625 Factor a perfect square on the left side: (X + 4.75)(X + 4.75) = 34.5625 Calculate the square root of the right side: 5.878988008 Break this problem into two subproblems by setting (X + 4.75) equal to 5.878988008 and -5.878988008.Subproblem 1
X + 4.75 = 5.878988008 Simplifying X + 4.75 = 5.878988008 Reorder the terms: 4.75 + X = 5.878988008 Solving 4.75 + X = 5.878988008 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + X = 5.878988008 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + X = 5.878988008 + -4.75 X = 5.878988008 + -4.75 Combine like terms: 5.878988008 + -4.75 = 1.128988008 X = 1.128988008 Simplifying X = 1.128988008Subproblem 2
X + 4.75 = -5.878988008 Simplifying X + 4.75 = -5.878988008 Reorder the terms: 4.75 + X = -5.878988008 Solving 4.75 + X = -5.878988008 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + X = -5.878988008 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + X = -5.878988008 + -4.75 X = -5.878988008 + -4.75 Combine like terms: -5.878988008 + -4.75 = -10.628988008 X = -10.628988008 Simplifying X = -10.628988008Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.128988008, -10.628988008}Solution
X = {1.128988008, -10.628988008}
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