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Simplifying -16t2 + 90t + 4 = 0 Reorder the terms: 4 + 90t + -16t2 = 0 Solving 4 + 90t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(2 + 45t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + 45t + -8t2)' equal to zero and attempt to solve: Simplifying 2 + 45t + -8t2 = 0 Solving 2 + 45t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.25 + -5.625t + t2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -5.625t + 0.25 + t2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -5.625t + t2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -5.625t + t2 = 0 + 0.25 -5.625t + t2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -5.625t + t2 = 0.25 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 = 0.25 + 7.91015625 Reorder the terms: 7.91015625 + -5.625t + t2 = 0.25 + 7.91015625 Combine like terms: 0.25 + 7.91015625 = 8.16015625 7.91015625 + -5.625t + t2 = 8.16015625 Factor a perfect square on the left side: (t + -2.8125)(t + -2.8125) = 8.16015625 Calculate the square root of the right side: 2.856598721 Break this problem into two subproblems by setting (t + -2.8125) equal to 2.856598721 and -2.856598721.Subproblem 1
t + -2.8125 = 2.856598721 Simplifying t + -2.8125 = 2.856598721 Reorder the terms: -2.8125 + t = 2.856598721 Solving -2.8125 + t = 2.856598721 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 = 2.856598721 + 2.8125 Combine like terms: -2.8125 + 2.8125 = 0.0000 0.0000 + t = 2.856598721 + 2.8125 t = 2.856598721 + 2.8125 Combine like terms: 2.856598721 + 2.8125 = 5.669098721 t = 5.669098721 Simplifying t = 5.669098721Subproblem 2
t + -2.8125 = -2.856598721 Simplifying t + -2.8125 = -2.856598721 Reorder the terms: -2.8125 + t = -2.856598721 Solving -2.8125 + t = -2.856598721 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 = -2.856598721 + 2.8125 Combine like terms: -2.8125 + 2.8125 = 0.0000 0.0000 + t = -2.856598721 + 2.8125 t = -2.856598721 + 2.8125 Combine like terms: -2.856598721 + 2.8125 = -0.044098721 t = -0.044098721 Simplifying t = -0.044098721Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.669098721, -0.044098721}Solution
t = {5.669098721, -0.044098721}
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