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Simplifying 100 = -16t2 + -12t Reorder the terms: 100 = -12t + -16t2 Solving 100 = -12t + -16t2 Solving for variable 't'. Reorder the terms: 100 + 12t + 16t2 = -12t + 12t + -16t2 + 16t2 Combine like terms: -12t + 12t = 0 100 + 12t + 16t2 = 0 + -16t2 + 16t2 100 + 12t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 100 + 12t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(25 + 3t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(25 + 3t + 4t2)' equal to zero and attempt to solve: Simplifying 25 + 3t + 4t2 = 0 Solving 25 + 3t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 6.25 + 0.75t + t2 = 0 Move the constant term to the right: Add '-6.25' to each side of the equation. 6.25 + 0.75t + -6.25 + t2 = 0 + -6.25 Reorder the terms: 6.25 + -6.25 + 0.75t + t2 = 0 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + 0.75t + t2 = 0 + -6.25 0.75t + t2 = 0 + -6.25 Combine like terms: 0 + -6.25 = -6.25 0.75t + t2 = -6.25 The t term is 0.75t. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75t + 0.140625 + t2 = -6.25 + 0.140625 Reorder the terms: 0.140625 + 0.75t + t2 = -6.25 + 0.140625 Combine like terms: -6.25 + 0.140625 = -6.109375 0.140625 + 0.75t + t2 = -6.109375 Factor a perfect square on the left side: (t + 0.375)(t + 0.375) = -6.109375 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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