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Simplifying -4(-16t2 + -2t + -90) = 0 Reorder the terms: -4(-90 + -2t + -16t2) = 0 (-90 * -4 + -2t * -4 + -16t2 * -4) = 0 (360 + 8t + 64t2) = 0 Solving 360 + 8t + 64t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '8'. 8(45 + t + 8t2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(45 + t + 8t2)' equal to zero and attempt to solve: Simplifying 45 + t + 8t2 = 0 Solving 45 + t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 5.625 + 0.125t + t2 = 0 Move the constant term to the right: Add '-5.625' to each side of the equation. 5.625 + 0.125t + -5.625 + t2 = 0 + -5.625 Reorder the terms: 5.625 + -5.625 + 0.125t + t2 = 0 + -5.625 Combine like terms: 5.625 + -5.625 = 0.000 0.000 + 0.125t + t2 = 0 + -5.625 0.125t + t2 = 0 + -5.625 Combine like terms: 0 + -5.625 = -5.625 0.125t + t2 = -5.625 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 = -5.625 + 0.25 Reorder the terms: 0.25 + 0.125t + t2 = -5.625 + 0.25 Combine like terms: -5.625 + 0.25 = -5.375 0.25 + 0.125t + t2 = -5.375 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = -5.375 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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