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Simplifying 12 = 12t + -16t2 Solving 12 = 12t + -16t2 Solving for variable 't'. Reorder the terms: 12 + -12t + 16t2 = 12t + -12t + -16t2 + 16t2 Combine like terms: 12t + -12t = 0 12 + -12t + 16t2 = 0 + -16t2 + 16t2 12 + -12t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 12 + -12t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(3 + -3t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(3 + -3t + 4t2)' equal to zero and attempt to solve: Simplifying 3 + -3t + 4t2 = 0 Solving 3 + -3t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.75 + -0.75t + t2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + -0.75t + -0.75 + t2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + -0.75t + t2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + -0.75t + t2 = 0 + -0.75 -0.75t + t2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 -0.75t + t2 = -0.75 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 = -0.75 + 0.140625 Reorder the terms: 0.140625 + -0.75t + t2 = -0.75 + 0.140625 Combine like terms: -0.75 + 0.140625 = -0.609375 0.140625 + -0.75t + t2 = -0.609375 Factor a perfect square on the left side: (t + -0.375)(t + -0.375) = -0.609375 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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