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Simplifying -16t2 + 90t = 34 Reorder the terms: 90t + -16t2 = 34 Solving 90t + -16t2 = 34 Solving for variable 't'. Reorder the terms: -34 + 90t + -16t2 = 34 + -34 Combine like terms: 34 + -34 = 0 -34 + 90t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-17 + 45t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-17 + 45t + -8t2)' equal to zero and attempt to solve: Simplifying -17 + 45t + -8t2 = 0 Solving -17 + 45t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 2.125 + -5.625t + t2 = 0 Move the constant term to the right: Add '-2.125' to each side of the equation. 2.125 + -5.625t + -2.125 + t2 = 0 + -2.125 Reorder the terms: 2.125 + -2.125 + -5.625t + t2 = 0 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + -5.625t + t2 = 0 + -2.125 -5.625t + t2 = 0 + -2.125 Combine like terms: 0 + -2.125 = -2.125 -5.625t + t2 = -2.125 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 = -2.125 + 7.91015625 Reorder the terms: 7.91015625 + -5.625t + t2 = -2.125 + 7.91015625 Combine like terms: -2.125 + 7.91015625 = 5.78515625 7.91015625 + -5.625t + t2 = 5.78515625 Factor a perfect square on the left side: (t + -2.8125)(t + -2.8125) = 5.78515625 Calculate the square root of the right side: 2.405235176 Break this problem into two subproblems by setting (t + -2.8125) equal to 2.405235176 and -2.405235176.Subproblem 1
t + -2.8125 = 2.405235176 Simplifying t + -2.8125 = 2.405235176 Reorder the terms: -2.8125 + t = 2.405235176 Solving -2.8125 + t = 2.405235176 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 = 2.405235176 + 2.8125 Combine like terms: -2.8125 + 2.8125 = 0.0000 0.0000 + t = 2.405235176 + 2.8125 t = 2.405235176 + 2.8125 Combine like terms: 2.405235176 + 2.8125 = 5.217735176 t = 5.217735176 Simplifying t = 5.217735176Subproblem 2
t + -2.8125 = -2.405235176 Simplifying t + -2.8125 = -2.405235176 Reorder the terms: -2.8125 + t = -2.405235176 Solving -2.8125 + t = -2.405235176 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 = -2.405235176 + 2.8125 Combine like terms: -2.8125 + 2.8125 = 0.0000 0.0000 + t = -2.405235176 + 2.8125 t = -2.405235176 + 2.8125 Combine like terms: -2.405235176 + 2.8125 = 0.407264824 t = 0.407264824 Simplifying t = 0.407264824Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.217735176, 0.407264824}Solution
t = {5.217735176, 0.407264824}
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