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Simplifying 0 = -16t2 + 90t + 6 Reorder the terms: 0 = 6 + 90t + -16t2 Solving 0 = 6 + 90t + -16t2 Solving for variable 't'. Combine like terms: 0 + -6 = -6 -6 + -90t + 16t2 = 6 + 90t + -16t2 + -6 + -90t + 16t2 Reorder the terms: -6 + -90t + 16t2 = 6 + -6 + 90t + -90t + -16t2 + 16t2 Combine like terms: 6 + -6 = 0 -6 + -90t + 16t2 = 0 + 90t + -90t + -16t2 + 16t2 -6 + -90t + 16t2 = 90t + -90t + -16t2 + 16t2 Combine like terms: 90t + -90t = 0 -6 + -90t + 16t2 = 0 + -16t2 + 16t2 -6 + -90t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -6 + -90t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + -45t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -45t + 8t2)' equal to zero and attempt to solve: Simplifying -3 + -45t + 8t2 = 0 Solving -3 + -45t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.375 + -5.625t + t2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -5.625t + 0.375 + t2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -5.625t + t2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -5.625t + t2 = 0 + 0.375 -5.625t + t2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -5.625t + t2 = 0.375 The t term is -5.625t. Take half its coefficient (-2.8125). Square it (7.91015625) and add it to both sides. Add '7.91015625' to each side of the equation. -5.625t + 7.91015625 + t2 = 0.375 + 7.91015625 Reorder the terms: 7.91015625 + -5.625t + t2 = 0.375 + 7.91015625 Combine like terms: 0.375 + 7.91015625 = 8.28515625 7.91015625 + -5.625t + t2 = 8.28515625 Factor a perfect square on the left side: (t + -2.8125)(t + -2.8125) = 8.28515625 Calculate the square root of the right side: 2.878394735 Break this problem into two subproblems by setting (t + -2.8125) equal to 2.878394735 and -2.878394735.Subproblem 1
t + -2.8125 = 2.878394735 Simplifying t + -2.8125 = 2.878394735 Reorder the terms: -2.8125 + t = 2.878394735 Solving -2.8125 + t = 2.878394735 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.8125' to each side of the equation. -2.8125 + 2.8125 + t = 2.878394735 + 2.8125 Combine like terms: -2.8125 + 2.8125 = 0.0000 0.0000 + t = 2.878394735 + 2.8125 t = 2.878394735 + 2.8125 Combine like terms: 2.878394735 + 2.8125 = 5.690894735 t = 5.690894735 Simplifying t = 5.690894735Subproblem 2
t + -2.8125 = -2.878394735 Simplifying t + -2.8125 = -2.878394735 Reorder the terms: -2.8125 + t = -2.878394735 Solving -2.8125 + t = -2.878394735 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.8125' to each side of the equation. -2.8125 + 2.8125 + t = -2.878394735 + 2.8125 Combine like terms: -2.8125 + 2.8125 = 0.0000 0.0000 + t = -2.878394735 + 2.8125 t = -2.878394735 + 2.8125 Combine like terms: -2.878394735 + 2.8125 = -0.065894735 t = -0.065894735 Simplifying t = -0.065894735Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.690894735, -0.065894735}Solution
t = {5.690894735, -0.065894735}
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