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Simplifying 0 = 24x2 + 2x + 8 Reorder the terms: 0 = 8 + 2x + 24x2 Solving 0 = 8 + 2x + 24x2 Solving for variable 'x'. Combine like terms: 0 + -8 = -8 -8 + -2x + -24x2 = 8 + 2x + 24x2 + -8 + -2x + -24x2 Reorder the terms: -8 + -2x + -24x2 = 8 + -8 + 2x + -2x + 24x2 + -24x2 Combine like terms: 8 + -8 = 0 -8 + -2x + -24x2 = 0 + 2x + -2x + 24x2 + -24x2 -8 + -2x + -24x2 = 2x + -2x + 24x2 + -24x2 Combine like terms: 2x + -2x = 0 -8 + -2x + -24x2 = 0 + 24x2 + -24x2 -8 + -2x + -24x2 = 24x2 + -24x2 Combine like terms: 24x2 + -24x2 = 0 -8 + -2x + -24x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(4 + x + 12x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(4 + x + 12x2)' equal to zero and attempt to solve: Simplifying 4 + x + 12x2 = 0 Solving 4 + x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.3333333333 + 0.08333333333x + x2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + 0.08333333333x + -0.3333333333 + x2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + 0.08333333333x + x2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + 0.08333333333x + x2 = 0 + -0.3333333333 0.08333333333x + x2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 0.08333333333x + x2 = -0.3333333333 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. 0.08333333333x + 0.25 + x2 = -0.3333333333 + 0.25 Reorder the terms: 0.25 + 0.08333333333x + x2 = -0.3333333333 + 0.25 Combine like terms: -0.3333333333 + 0.25 = -0.0833333333 0.25 + 0.08333333333x + x2 = -0.0833333333 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -0.0833333333 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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