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Simplifying 16x2 + 8x + 48 = 0 Reorder the terms: 48 + 8x + 16x2 = 0 Solving 48 + 8x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '8'. 8(6 + x + 2x2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(6 + x + 2x2)' equal to zero and attempt to solve: Simplifying 6 + x + 2x2 = 0 Solving 6 + x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3 + 0.5x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + 0.5x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + 0.5x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 0.5x + x2 = 0 + -3 0.5x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 0.5x + x2 = -3 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. 0.5x + 0.25 + x2 = -3 + 0.25 Reorder the terms: 0.25 + 0.5x + x2 = -3 + 0.25 Combine like terms: -3 + 0.25 = -2.75 0.25 + 0.5x + x2 = -2.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -2.75 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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