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Simplifying -16t2 + 21.3t + 80 = 0 Reorder the terms: 80 + 21.3t + -16t2 = 0 Solving 80 + 21.3t + -16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -5 + -1.33125t + t2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -1.33125t + 5 + t2 = 0 + 5 Reorder the terms: -5 + 5 + -1.33125t + t2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1.33125t + t2 = 0 + 5 -1.33125t + t2 = 0 + 5 Combine like terms: 0 + 5 = 5 -1.33125t + t2 = 5 The t term is -1.33125t. Take half its coefficient (-0.665625). Square it (0.4430566406) and add it to both sides. Add '0.4430566406' to each side of the equation. -1.33125t + 0.4430566406 + t2 = 5 + 0.4430566406 Reorder the terms: 0.4430566406 + -1.33125t + t2 = 5 + 0.4430566406 Combine like terms: 5 + 0.4430566406 = 5.4430566406 0.4430566406 + -1.33125t + t2 = 5.4430566406 Factor a perfect square on the left side: (t + -0.665625)(t + -0.665625) = 5.4430566406 Calculate the square root of the right side: 2.333035928 Break this problem into two subproblems by setting (t + -0.665625) equal to 2.333035928 and -2.333035928.Subproblem 1
t + -0.665625 = 2.333035928 Simplifying t + -0.665625 = 2.333035928 Reorder the terms: -0.665625 + t = 2.333035928 Solving -0.665625 + t = 2.333035928 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.665625' to each side of the equation. -0.665625 + 0.665625 + t = 2.333035928 + 0.665625 Combine like terms: -0.665625 + 0.665625 = 0.000000 0.000000 + t = 2.333035928 + 0.665625 t = 2.333035928 + 0.665625 Combine like terms: 2.333035928 + 0.665625 = 2.998660928 t = 2.998660928 Simplifying t = 2.998660928Subproblem 2
t + -0.665625 = -2.333035928 Simplifying t + -0.665625 = -2.333035928 Reorder the terms: -0.665625 + t = -2.333035928 Solving -0.665625 + t = -2.333035928 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.665625' to each side of the equation. -0.665625 + 0.665625 + t = -2.333035928 + 0.665625 Combine like terms: -0.665625 + 0.665625 = 0.000000 0.000000 + t = -2.333035928 + 0.665625 t = -2.333035928 + 0.665625 Combine like terms: -2.333035928 + 0.665625 = -1.667410928 t = -1.667410928 Simplifying t = -1.667410928Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.998660928, -1.667410928}
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