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Simplifying -16t2 + 109t + 90 = 0 Reorder the terms: 90 + 109t + -16t2 = 0 Solving 90 + 109t + -16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -5.625 + -6.8125t + t2 = 0 Move the constant term to the right: Add '5.625' to each side of the equation. -5.625 + -6.8125t + 5.625 + t2 = 0 + 5.625 Reorder the terms: -5.625 + 5.625 + -6.8125t + t2 = 0 + 5.625 Combine like terms: -5.625 + 5.625 = 0.000 0.000 + -6.8125t + t2 = 0 + 5.625 -6.8125t + t2 = 0 + 5.625 Combine like terms: 0 + 5.625 = 5.625 -6.8125t + t2 = 5.625 The t term is -6.8125t. Take half its coefficient (-3.40625). Square it (11.60253906) and add it to both sides. Add '11.60253906' to each side of the equation. -6.8125t + 11.60253906 + t2 = 5.625 + 11.60253906 Reorder the terms: 11.60253906 + -6.8125t + t2 = 5.625 + 11.60253906 Combine like terms: 5.625 + 11.60253906 = 17.22753906 11.60253906 + -6.8125t + t2 = 17.22753906 Factor a perfect square on the left side: (t + -3.40625)(t + -3.40625) = 17.22753906 Calculate the square root of the right side: 4.150607071 Break this problem into two subproblems by setting (t + -3.40625) equal to 4.150607071 and -4.150607071.Subproblem 1
t + -3.40625 = 4.150607071 Simplifying t + -3.40625 = 4.150607071 Reorder the terms: -3.40625 + t = 4.150607071 Solving -3.40625 + t = 4.150607071 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.40625' to each side of the equation. -3.40625 + 3.40625 + t = 4.150607071 + 3.40625 Combine like terms: -3.40625 + 3.40625 = 0.00000 0.00000 + t = 4.150607071 + 3.40625 t = 4.150607071 + 3.40625 Combine like terms: 4.150607071 + 3.40625 = 7.556857071 t = 7.556857071 Simplifying t = 7.556857071Subproblem 2
t + -3.40625 = -4.150607071 Simplifying t + -3.40625 = -4.150607071 Reorder the terms: -3.40625 + t = -4.150607071 Solving -3.40625 + t = -4.150607071 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.40625' to each side of the equation. -3.40625 + 3.40625 + t = -4.150607071 + 3.40625 Combine like terms: -3.40625 + 3.40625 = 0.00000 0.00000 + t = -4.150607071 + 3.40625 t = -4.150607071 + 3.40625 Combine like terms: -4.150607071 + 3.40625 = -0.744357071 t = -0.744357071 Simplifying t = -0.744357071Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.556857071, -0.744357071}
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