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Simplifying 8 = -16t2 + 22t + -8 Reorder the terms: 8 = -8 + 22t + -16t2 Solving 8 = -8 + 22t + -16t2 Solving for variable 't'. Combine like terms: 8 + 8 = 16 16 + -22t + 16t2 = -8 + 22t + -16t2 + 8 + -22t + 16t2 Reorder the terms: 16 + -22t + 16t2 = -8 + 8 + 22t + -22t + -16t2 + 16t2 Combine like terms: -8 + 8 = 0 16 + -22t + 16t2 = 0 + 22t + -22t + -16t2 + 16t2 16 + -22t + 16t2 = 22t + -22t + -16t2 + 16t2 Combine like terms: 22t + -22t = 0 16 + -22t + 16t2 = 0 + -16t2 + 16t2 16 + -22t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 16 + -22t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(8 + -11t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(8 + -11t + 8t2)' equal to zero and attempt to solve: Simplifying 8 + -11t + 8t2 = 0 Solving 8 + -11t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1 + -1.375t + t2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -1.375t + -1 + t2 = 0 + -1 Reorder the terms: 1 + -1 + -1.375t + t2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1.375t + t2 = 0 + -1 -1.375t + t2 = 0 + -1 Combine like terms: 0 + -1 = -1 -1.375t + t2 = -1 The t term is -1.375t. Take half its coefficient (-0.6875). Square it (0.47265625) and add it to both sides. Add '0.47265625' to each side of the equation. -1.375t + 0.47265625 + t2 = -1 + 0.47265625 Reorder the terms: 0.47265625 + -1.375t + t2 = -1 + 0.47265625 Combine like terms: -1 + 0.47265625 = -0.52734375 0.47265625 + -1.375t + t2 = -0.52734375 Factor a perfect square on the left side: (t + -0.6875)(t + -0.6875) = -0.52734375 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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