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Simplifying 2X2 + -56X + -176 = 0 Reorder the terms: -176 + -56X + 2X2 = 0 Solving -176 + -56X + 2X2 = 0 Solving for variable 'X'. Factor out the Greatest Common Factor (GCF), '2'. 2(-88 + -28X + X2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-88 + -28X + X2)' equal to zero and attempt to solve: Simplifying -88 + -28X + X2 = 0 Solving -88 + -28X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '88' to each side of the equation. -88 + -28X + 88 + X2 = 0 + 88 Reorder the terms: -88 + 88 + -28X + X2 = 0 + 88 Combine like terms: -88 + 88 = 0 0 + -28X + X2 = 0 + 88 -28X + X2 = 0 + 88 Combine like terms: 0 + 88 = 88 -28X + X2 = 88 The X term is -28X. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28X + 196 + X2 = 88 + 196 Reorder the terms: 196 + -28X + X2 = 88 + 196 Combine like terms: 88 + 196 = 284 196 + -28X + X2 = 284 Factor a perfect square on the left side: (X + -14)(X + -14) = 284 Calculate the square root of the right side: 16.852299546 Break this problem into two subproblems by setting (X + -14) equal to 16.852299546 and -16.852299546.Subproblem 1
X + -14 = 16.852299546 Simplifying X + -14 = 16.852299546 Reorder the terms: -14 + X = 16.852299546 Solving -14 + X = 16.852299546 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + X = 16.852299546 + 14 Combine like terms: -14 + 14 = 0 0 + X = 16.852299546 + 14 X = 16.852299546 + 14 Combine like terms: 16.852299546 + 14 = 30.852299546 X = 30.852299546 Simplifying X = 30.852299546Subproblem 2
X + -14 = -16.852299546 Simplifying X + -14 = -16.852299546 Reorder the terms: -14 + X = -16.852299546 Solving -14 + X = -16.852299546 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + X = -16.852299546 + 14 Combine like terms: -14 + 14 = 0 0 + X = -16.852299546 + 14 X = -16.852299546 + 14 Combine like terms: -16.852299546 + 14 = -2.852299546 X = -2.852299546 Simplifying X = -2.852299546Solution
The solution to the problem is based on the solutions from the subproblems. X = {30.852299546, -2.852299546}Solution
X = {30.852299546, -2.852299546}
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