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Simplifying 2x2 + 8x + -322 = 0 Reorder the terms: -322 + 8x + 2x2 = 0 Solving -322 + 8x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-161 + 4x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-161 + 4x + x2)' equal to zero and attempt to solve: Simplifying -161 + 4x + x2 = 0 Solving -161 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '161' to each side of the equation. -161 + 4x + 161 + x2 = 0 + 161 Reorder the terms: -161 + 161 + 4x + x2 = 0 + 161 Combine like terms: -161 + 161 = 0 0 + 4x + x2 = 0 + 161 4x + x2 = 0 + 161 Combine like terms: 0 + 161 = 161 4x + x2 = 161 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 = 161 + 4 Reorder the terms: 4 + 4x + x2 = 161 + 4 Combine like terms: 161 + 4 = 165 4 + 4x + x2 = 165 Factor a perfect square on the left side: (x + 2)(x + 2) = 165 Calculate the square root of the right side: 12.845232579 Break this problem into two subproblems by setting (x + 2) equal to 12.845232579 and -12.845232579.Subproblem 1
x + 2 = 12.845232579 Simplifying x + 2 = 12.845232579 Reorder the terms: 2 + x = 12.845232579 Solving 2 + x = 12.845232579 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 = 12.845232579 + -2 Combine like terms: 2 + -2 = 0 0 + x = 12.845232579 + -2 x = 12.845232579 + -2 Combine like terms: 12.845232579 + -2 = 10.845232579 x = 10.845232579 Simplifying x = 10.845232579Subproblem 2
x + 2 = -12.845232579 Simplifying x + 2 = -12.845232579 Reorder the terms: 2 + x = -12.845232579 Solving 2 + x = -12.845232579 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 = -12.845232579 + -2 Combine like terms: 2 + -2 = 0 0 + x = -12.845232579 + -2 x = -12.845232579 + -2 Combine like terms: -12.845232579 + -2 = -14.845232579 x = -14.845232579 Simplifying x = -14.845232579Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.845232579, -14.845232579}Solution
x = {10.845232579, -14.845232579}
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