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Simplifying 124 = -16t2 + -30t + 484 Reorder the terms: 124 = 484 + -30t + -16t2 Solving 124 = 484 + -30t + -16t2 Solving for variable 't'. Combine like terms: 124 + -484 = -360 -360 + 30t + 16t2 = 484 + -30t + -16t2 + -484 + 30t + 16t2 Reorder the terms: -360 + 30t + 16t2 = 484 + -484 + -30t + 30t + -16t2 + 16t2 Combine like terms: 484 + -484 = 0 -360 + 30t + 16t2 = 0 + -30t + 30t + -16t2 + 16t2 -360 + 30t + 16t2 = -30t + 30t + -16t2 + 16t2 Combine like terms: -30t + 30t = 0 -360 + 30t + 16t2 = 0 + -16t2 + 16t2 -360 + 30t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -360 + 30t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-180 + 15t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-180 + 15t + 8t2)' equal to zero and attempt to solve: Simplifying -180 + 15t + 8t2 = 0 Solving -180 + 15t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -22.5 + 1.875t + t2 = 0 Move the constant term to the right: Add '22.5' to each side of the equation. -22.5 + 1.875t + 22.5 + t2 = 0 + 22.5 Reorder the terms: -22.5 + 22.5 + 1.875t + t2 = 0 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + 1.875t + t2 = 0 + 22.5 1.875t + t2 = 0 + 22.5 Combine like terms: 0 + 22.5 = 22.5 1.875t + t2 = 22.5 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 = 22.5 + 0.87890625 Reorder the terms: 0.87890625 + 1.875t + t2 = 22.5 + 0.87890625 Combine like terms: 22.5 + 0.87890625 = 23.37890625 0.87890625 + 1.875t + t2 = 23.37890625 Factor a perfect square on the left side: (t + 0.9375)(t + 0.9375) = 23.37890625 Calculate the square root of the right side: 4.835173859 Break this problem into two subproblems by setting (t + 0.9375) equal to 4.835173859 and -4.835173859.Subproblem 1
t + 0.9375 = 4.835173859 Simplifying t + 0.9375 = 4.835173859 Reorder the terms: 0.9375 + t = 4.835173859 Solving 0.9375 + t = 4.835173859 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 = 4.835173859 + -0.9375 Combine like terms: 0.9375 + -0.9375 = 0.0000 0.0000 + t = 4.835173859 + -0.9375 t = 4.835173859 + -0.9375 Combine like terms: 4.835173859 + -0.9375 = 3.897673859 t = 3.897673859 Simplifying t = 3.897673859Subproblem 2
t + 0.9375 = -4.835173859 Simplifying t + 0.9375 = -4.835173859 Reorder the terms: 0.9375 + t = -4.835173859 Solving 0.9375 + t = -4.835173859 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 = -4.835173859 + -0.9375 Combine like terms: 0.9375 + -0.9375 = 0.0000 0.0000 + t = -4.835173859 + -0.9375 t = -4.835173859 + -0.9375 Combine like terms: -4.835173859 + -0.9375 = -5.772673859 t = -5.772673859 Simplifying t = -5.772673859Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.897673859, -5.772673859}Solution
t = {3.897673859, -5.772673859}
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