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Simplifying -16t2 + 90t + 30 = 0 Reorder the terms: 30 + 90t + -16t2 = 0 Solving 30 + 90t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(15 + 45t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(15 + 45t + -8t2)' equal to zero and attempt to solve: Simplifying 15 + 45t + -8t2 = 0 Solving 15 + 45t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -1.875 + -5.625t + t2 = 0 Move the constant term to the right: Add '1.875' to each side of the equation. -1.875 + -5.625t + 1.875 + t2 = 0 + 1.875 Reorder the terms: -1.875 + 1.875 + -5.625t + t2 = 0 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + -5.625t + t2 = 0 + 1.875 -5.625t + t2 = 0 + 1.875 Combine like terms: 0 + 1.875 = 1.875 -5.625t + t2 = 1.875 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 = 1.875 + 7.91015625 Reorder the terms: 7.91015625 + -5.625t + t2 = 1.875 + 7.91015625 Combine like terms: 1.875 + 7.91015625 = 9.78515625 7.91015625 + -5.625t + t2 = 9.78515625 Factor a perfect square on the left side: (t + -2.8125)(t + -2.8125) = 9.78515625 Calculate the square root of the right side: 3.128123439 Break this problem into two subproblems by setting (t + -2.8125) equal to 3.128123439 and -3.128123439.Subproblem 1
t + -2.8125 = 3.128123439 Simplifying t + -2.8125 = 3.128123439 Reorder the terms: -2.8125 + t = 3.128123439 Solving -2.8125 + t = 3.128123439 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 = 3.128123439 + 2.8125 Combine like terms: -2.8125 + 2.8125 = 0.0000 0.0000 + t = 3.128123439 + 2.8125 t = 3.128123439 + 2.8125 Combine like terms: 3.128123439 + 2.8125 = 5.940623439 t = 5.940623439 Simplifying t = 5.940623439Subproblem 2
t + -2.8125 = -3.128123439 Simplifying t + -2.8125 = -3.128123439 Reorder the terms: -2.8125 + t = -3.128123439 Solving -2.8125 + t = -3.128123439 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 = -3.128123439 + 2.8125 Combine like terms: -2.8125 + 2.8125 = 0.0000 0.0000 + t = -3.128123439 + 2.8125 t = -3.128123439 + 2.8125 Combine like terms: -3.128123439 + 2.8125 = -0.315623439 t = -0.315623439 Simplifying t = -0.315623439Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.940623439, -0.315623439}Solution
t = {5.940623439, -0.315623439}
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