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Simplifying 0 = 750 + -9t + -16t2 Solving 0 = 750 + -9t + -16t2 Solving for variable 't'. Combine like terms: 0 + -750 = -750 -750 + 9t + 16t2 = 750 + -9t + -16t2 + -750 + 9t + 16t2 Reorder the terms: -750 + 9t + 16t2 = 750 + -750 + -9t + 9t + -16t2 + 16t2 Combine like terms: 750 + -750 = 0 -750 + 9t + 16t2 = 0 + -9t + 9t + -16t2 + 16t2 -750 + 9t + 16t2 = -9t + 9t + -16t2 + 16t2 Combine like terms: -9t + 9t = 0 -750 + 9t + 16t2 = 0 + -16t2 + 16t2 -750 + 9t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -750 + 9t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -46.875 + 0.5625t + t2 = 0 Move the constant term to the right: Add '46.875' to each side of the equation. -46.875 + 0.5625t + 46.875 + t2 = 0 + 46.875 Reorder the terms: -46.875 + 46.875 + 0.5625t + t2 = 0 + 46.875 Combine like terms: -46.875 + 46.875 = 0.000 0.000 + 0.5625t + t2 = 0 + 46.875 0.5625t + t2 = 0 + 46.875 Combine like terms: 0 + 46.875 = 46.875 0.5625t + t2 = 46.875 The t term is 0.5625t. Take half its coefficient (0.28125). Square it (0.0791015625) and add it to both sides. Add '0.0791015625' to each side of the equation. 0.5625t + 0.0791015625 + t2 = 46.875 + 0.0791015625 Reorder the terms: 0.0791015625 + 0.5625t + t2 = 46.875 + 0.0791015625 Combine like terms: 46.875 + 0.0791015625 = 46.9541015625 0.0791015625 + 0.5625t + t2 = 46.9541015625 Factor a perfect square on the left side: (t + 0.28125)(t + 0.28125) = 46.9541015625 Calculate the square root of the right side: 6.852306295 Break this problem into two subproblems by setting (t + 0.28125) equal to 6.852306295 and -6.852306295.Subproblem 1
t + 0.28125 = 6.852306295 Simplifying t + 0.28125 = 6.852306295 Reorder the terms: 0.28125 + t = 6.852306295 Solving 0.28125 + t = 6.852306295 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.28125' to each side of the equation. 0.28125 + -0.28125 + t = 6.852306295 + -0.28125 Combine like terms: 0.28125 + -0.28125 = 0.00000 0.00000 + t = 6.852306295 + -0.28125 t = 6.852306295 + -0.28125 Combine like terms: 6.852306295 + -0.28125 = 6.571056295 t = 6.571056295 Simplifying t = 6.571056295Subproblem 2
t + 0.28125 = -6.852306295 Simplifying t + 0.28125 = -6.852306295 Reorder the terms: 0.28125 + t = -6.852306295 Solving 0.28125 + t = -6.852306295 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.28125' to each side of the equation. 0.28125 + -0.28125 + t = -6.852306295 + -0.28125 Combine like terms: 0.28125 + -0.28125 = 0.00000 0.00000 + t = -6.852306295 + -0.28125 t = -6.852306295 + -0.28125 Combine like terms: -6.852306295 + -0.28125 = -7.133556295 t = -7.133556295 Simplifying t = -7.133556295Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.571056295, -7.133556295}
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