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Simplifying 98 = 16t2 + 2t + 112 Reorder the terms: 98 = 112 + 2t + 16t2 Solving 98 = 112 + 2t + 16t2 Solving for variable 't'. Combine like terms: 98 + -112 = -14 -14 + -2t + -16t2 = 112 + 2t + 16t2 + -112 + -2t + -16t2 Reorder the terms: -14 + -2t + -16t2 = 112 + -112 + 2t + -2t + 16t2 + -16t2 Combine like terms: 112 + -112 = 0 -14 + -2t + -16t2 = 0 + 2t + -2t + 16t2 + -16t2 -14 + -2t + -16t2 = 2t + -2t + 16t2 + -16t2 Combine like terms: 2t + -2t = 0 -14 + -2t + -16t2 = 0 + 16t2 + -16t2 -14 + -2t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -14 + -2t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(7 + t + 8t2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(7 + t + 8t2)' equal to zero and attempt to solve: Simplifying 7 + t + 8t2 = 0 Solving 7 + t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.875 + 0.125t + t2 = 0 Move the constant term to the right: Add '-0.875' to each side of the equation. 0.875 + 0.125t + -0.875 + t2 = 0 + -0.875 Reorder the terms: 0.875 + -0.875 + 0.125t + t2 = 0 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + 0.125t + t2 = 0 + -0.875 0.125t + t2 = 0 + -0.875 Combine like terms: 0 + -0.875 = -0.875 0.125t + t2 = -0.875 The t term is t. 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. 0.125t + 0.25 + t2 = -0.875 + 0.25 Reorder the terms: 0.25 + 0.125t + t2 = -0.875 + 0.25 Combine like terms: -0.875 + 0.25 = -0.625 0.25 + 0.125t + t2 = -0.625 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = -0.625 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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