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Simplifying 16t2 + -90t + 90 = 0 Reorder the terms: 90 + -90t + 16t2 = 0 Solving 90 + -90t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(45 + -45t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(45 + -45t + 8t2)' equal to zero and attempt to solve: Simplifying 45 + -45t + 8t2 = 0 Solving 45 + -45t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 5.625 + -5.625t + t2 = 0 Move the constant term to the right: Add '-5.625' to each side of the equation. 5.625 + -5.625t + -5.625 + t2 = 0 + -5.625 Reorder the terms: 5.625 + -5.625 + -5.625t + t2 = 0 + -5.625 Combine like terms: 5.625 + -5.625 = 0.000 0.000 + -5.625t + t2 = 0 + -5.625 -5.625t + t2 = 0 + -5.625 Combine like terms: 0 + -5.625 = -5.625 -5.625t + t2 = -5.625 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 = -5.625 + 7.91015625 Reorder the terms: 7.91015625 + -5.625t + t2 = -5.625 + 7.91015625 Combine like terms: -5.625 + 7.91015625 = 2.28515625 7.91015625 + -5.625t + t2 = 2.28515625 Factor a perfect square on the left side: (t + -2.8125)(t + -2.8125) = 2.28515625 Calculate the square root of the right side: 1.511673328 Break this problem into two subproblems by setting (t + -2.8125) equal to 1.511673328 and -1.511673328.Subproblem 1
t + -2.8125 = 1.511673328 Simplifying t + -2.8125 = 1.511673328 Reorder the terms: -2.8125 + t = 1.511673328 Solving -2.8125 + t = 1.511673328 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 = 1.511673328 + 2.8125 Combine like terms: -2.8125 + 2.8125 = 0.0000 0.0000 + t = 1.511673328 + 2.8125 t = 1.511673328 + 2.8125 Combine like terms: 1.511673328 + 2.8125 = 4.324173328 t = 4.324173328 Simplifying t = 4.324173328Subproblem 2
t + -2.8125 = -1.511673328 Simplifying t + -2.8125 = -1.511673328 Reorder the terms: -2.8125 + t = -1.511673328 Solving -2.8125 + t = -1.511673328 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 = -1.511673328 + 2.8125 Combine like terms: -2.8125 + 2.8125 = 0.0000 0.0000 + t = -1.511673328 + 2.8125 t = -1.511673328 + 2.8125 Combine like terms: -1.511673328 + 2.8125 = 1.300826672 t = 1.300826672 Simplifying t = 1.300826672Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.324173328, 1.300826672}Solution
t = {4.324173328, 1.300826672}
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