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Simplifying -16t2 + 30t + 300 = 0 Reorder the terms: 300 + 30t + -16t2 = 0 Solving 300 + 30t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(150 + 15t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(150 + 15t + -8t2)' equal to zero and attempt to solve: Simplifying 150 + 15t + -8t2 = 0 Solving 150 + 15t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -18.75 + -1.875t + t2 = 0 Move the constant term to the right: Add '18.75' to each side of the equation. -18.75 + -1.875t + 18.75 + t2 = 0 + 18.75 Reorder the terms: -18.75 + 18.75 + -1.875t + t2 = 0 + 18.75 Combine like terms: -18.75 + 18.75 = 0.00 0.00 + -1.875t + t2 = 0 + 18.75 -1.875t + t2 = 0 + 18.75 Combine like terms: 0 + 18.75 = 18.75 -1.875t + t2 = 18.75 The t term is -1.875t. Take half its coefficient (-0.9375). Square it (0.87890625) and add it to both sides. Add '0.87890625' to each side of the equation. -1.875t + 0.87890625 + t2 = 18.75 + 0.87890625 Reorder the terms: 0.87890625 + -1.875t + t2 = 18.75 + 0.87890625 Combine like terms: 18.75 + 0.87890625 = 19.62890625 0.87890625 + -1.875t + t2 = 19.62890625 Factor a perfect square on the left side: (t + -0.9375)(t + -0.9375) = 19.62890625 Calculate the square root of the right side: 4.43045215 Break this problem into two subproblems by setting (t + -0.9375) equal to 4.43045215 and -4.43045215.Subproblem 1
t + -0.9375 = 4.43045215 Simplifying t + -0.9375 = 4.43045215 Reorder the terms: -0.9375 + t = 4.43045215 Solving -0.9375 + t = 4.43045215 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.9375' to each side of the equation. -0.9375 + 0.9375 + t = 4.43045215 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + t = 4.43045215 + 0.9375 t = 4.43045215 + 0.9375 Combine like terms: 4.43045215 + 0.9375 = 5.36795215 t = 5.36795215 Simplifying t = 5.36795215Subproblem 2
t + -0.9375 = -4.43045215 Simplifying t + -0.9375 = -4.43045215 Reorder the terms: -0.9375 + t = -4.43045215 Solving -0.9375 + t = -4.43045215 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.9375' to each side of the equation. -0.9375 + 0.9375 + t = -4.43045215 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + t = -4.43045215 + 0.9375 t = -4.43045215 + 0.9375 Combine like terms: -4.43045215 + 0.9375 = -3.49295215 t = -3.49295215 Simplifying t = -3.49295215Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.36795215, -3.49295215}Solution
t = {5.36795215, -3.49295215}
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