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Simplifying 45t = 16t2 + 55t + 6 Reorder the terms: 45t = 6 + 55t + 16t2 Solving 45t = 6 + 55t + 16t2 Solving for variable 't'. Reorder the terms: -6 + 45t + -55t + -16t2 = 6 + 55t + 16t2 + -6 + -55t + -16t2 Combine like terms: 45t + -55t = -10t -6 + -10t + -16t2 = 6 + 55t + 16t2 + -6 + -55t + -16t2 Reorder the terms: -6 + -10t + -16t2 = 6 + -6 + 55t + -55t + 16t2 + -16t2 Combine like terms: 6 + -6 = 0 -6 + -10t + -16t2 = 0 + 55t + -55t + 16t2 + -16t2 -6 + -10t + -16t2 = 55t + -55t + 16t2 + -16t2 Combine like terms: 55t + -55t = 0 -6 + -10t + -16t2 = 0 + 16t2 + -16t2 -6 + -10t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -6 + -10t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(3 + 5t + 8t2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(3 + 5t + 8t2)' equal to zero and attempt to solve: Simplifying 3 + 5t + 8t2 = 0 Solving 3 + 5t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.375 + 0.625t + t2 = 0 Move the constant term to the right: Add '-0.375' to each side of the equation. 0.375 + 0.625t + -0.375 + t2 = 0 + -0.375 Reorder the terms: 0.375 + -0.375 + 0.625t + t2 = 0 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + 0.625t + t2 = 0 + -0.375 0.625t + t2 = 0 + -0.375 Combine like terms: 0 + -0.375 = -0.375 0.625t + t2 = -0.375 The t term is 0.625t. Take half its coefficient (0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. 0.625t + 0.09765625 + t2 = -0.375 + 0.09765625 Reorder the terms: 0.09765625 + 0.625t + t2 = -0.375 + 0.09765625 Combine like terms: -0.375 + 0.09765625 = -0.27734375 0.09765625 + 0.625t + t2 = -0.27734375 Factor a perfect square on the left side: (t + 0.3125)(t + 0.3125) = -0.27734375 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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