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Simplifying 2x2 + 16x + 82 = 0 Reorder the terms: 82 + 16x + 2x2 = 0 Solving 82 + 16x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(41 + 8x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(41 + 8x + x2)' equal to zero and attempt to solve: Simplifying 41 + 8x + x2 = 0 Solving 41 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-41' to each side of the equation. 41 + 8x + -41 + x2 = 0 + -41 Reorder the terms: 41 + -41 + 8x + x2 = 0 + -41 Combine like terms: 41 + -41 = 0 0 + 8x + x2 = 0 + -41 8x + x2 = 0 + -41 Combine like terms: 0 + -41 = -41 8x + x2 = -41 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = -41 + 16 Reorder the terms: 16 + 8x + x2 = -41 + 16 Combine like terms: -41 + 16 = -25 16 + 8x + x2 = -25 Factor a perfect square on the left side: (x + 4)(x + 4) = -25 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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