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Simplifying 0 = 16t2 + 22t + 19 Reorder the terms: 0 = 19 + 22t + 16t2 Solving 0 = 19 + 22t + 16t2 Solving for variable 't'. Combine like terms: 0 + -19 = -19 -19 + -22t + -16t2 = 19 + 22t + 16t2 + -19 + -22t + -16t2 Reorder the terms: -19 + -22t + -16t2 = 19 + -19 + 22t + -22t + 16t2 + -16t2 Combine like terms: 19 + -19 = 0 -19 + -22t + -16t2 = 0 + 22t + -22t + 16t2 + -16t2 -19 + -22t + -16t2 = 22t + -22t + 16t2 + -16t2 Combine like terms: 22t + -22t = 0 -19 + -22t + -16t2 = 0 + 16t2 + -16t2 -19 + -22t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -19 + -22t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(19 + 22t + 16t2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(19 + 22t + 16t2)' equal to zero and attempt to solve: Simplifying 19 + 22t + 16t2 = 0 Solving 19 + 22t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 1.1875 + 1.375t + t2 = 0 Move the constant term to the right: Add '-1.1875' to each side of the equation. 1.1875 + 1.375t + -1.1875 + t2 = 0 + -1.1875 Reorder the terms: 1.1875 + -1.1875 + 1.375t + t2 = 0 + -1.1875 Combine like terms: 1.1875 + -1.1875 = 0.0000 0.0000 + 1.375t + t2 = 0 + -1.1875 1.375t + t2 = 0 + -1.1875 Combine like terms: 0 + -1.1875 = -1.1875 1.375t + t2 = -1.1875 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 = -1.1875 + 0.47265625 Reorder the terms: 0.47265625 + 1.375t + t2 = -1.1875 + 0.47265625 Combine like terms: -1.1875 + 0.47265625 = -0.71484375 0.47265625 + 1.375t + t2 = -0.71484375 Factor a perfect square on the left side: (t + 0.6875)(t + 0.6875) = -0.71484375 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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