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Simplifying 0 = 10X2 + X + 16 Reorder the terms: 0 = 16 + X + 10X2 Solving 0 = 16 + X + 10X2 Solving for variable 'X'. Combine like terms: 0 + -16 = -16 -16 + -1X + -10X2 = 16 + X + 10X2 + -16 + -1X + -10X2 Reorder the terms: -16 + -1X + -10X2 = 16 + -16 + X + -1X + 10X2 + -10X2 Combine like terms: 16 + -16 = 0 -16 + -1X + -10X2 = 0 + X + -1X + 10X2 + -10X2 -16 + -1X + -10X2 = X + -1X + 10X2 + -10X2 Combine like terms: X + -1X = 0 -16 + -1X + -10X2 = 0 + 10X2 + -10X2 -16 + -1X + -10X2 = 10X2 + -10X2 Combine like terms: 10X2 + -10X2 = 0 -16 + -1X + -10X2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(16 + X + 10X2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(16 + X + 10X2)' equal to zero and attempt to solve: Simplifying 16 + X + 10X2 = 0 Solving 16 + X + 10X2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 1.6 + 0.1X + X2 = 0.0 Move the constant term to the right: Add '-1.6' to each side of the equation. 1.6 + 0.1X + -1.6 + X2 = 0.0 + -1.6 Reorder the terms: 1.6 + -1.6 + 0.1X + X2 = 0.0 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + 0.1X + X2 = 0.0 + -1.6 0.1X + X2 = 0.0 + -1.6 Combine like terms: 0.0 + -1.6 = -1.6 0.1X + X2 = -1.6 The X term is X. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.1X + 0.25 + X2 = -1.6 + 0.25 Reorder the terms: 0.25 + 0.1X + X2 = -1.6 + 0.25 Combine like terms: -1.6 + 0.25 = -1.35 0.25 + 0.1X + X2 = -1.35 Factor a perfect square on the left side: (X + 0.5)(X + 0.5) = -1.35 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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