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Simplifying 30 = 64t + -16t2 Solving 30 = 64t + -16t2 Solving for variable 't'. Reorder the terms: 30 + -64t + 16t2 = 64t + -64t + -16t2 + 16t2 Combine like terms: 64t + -64t = 0 30 + -64t + 16t2 = 0 + -16t2 + 16t2 30 + -64t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 30 + -64t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(15 + -32t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(15 + -32t + 8t2)' equal to zero and attempt to solve: Simplifying 15 + -32t + 8t2 = 0 Solving 15 + -32t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.875 + -4t + t2 = 0 Move the constant term to the right: Add '-1.875' to each side of the equation. 1.875 + -4t + -1.875 + t2 = 0 + -1.875 Reorder the terms: 1.875 + -1.875 + -4t + t2 = 0 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + -4t + t2 = 0 + -1.875 -4t + t2 = 0 + -1.875 Combine like terms: 0 + -1.875 = -1.875 -4t + t2 = -1.875 The t term is -4t. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4t + 4 + t2 = -1.875 + 4 Reorder the terms: 4 + -4t + t2 = -1.875 + 4 Combine like terms: -1.875 + 4 = 2.125 4 + -4t + t2 = 2.125 Factor a perfect square on the left side: (t + -2)(t + -2) = 2.125 Calculate the square root of the right side: 1.457737974 Break this problem into two subproblems by setting (t + -2) equal to 1.457737974 and -1.457737974.Subproblem 1
t + -2 = 1.457737974 Simplifying t + -2 = 1.457737974 Reorder the terms: -2 + t = 1.457737974 Solving -2 + t = 1.457737974 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = 1.457737974 + 2 Combine like terms: -2 + 2 = 0 0 + t = 1.457737974 + 2 t = 1.457737974 + 2 Combine like terms: 1.457737974 + 2 = 3.457737974 t = 3.457737974 Simplifying t = 3.457737974Subproblem 2
t + -2 = -1.457737974 Simplifying t + -2 = -1.457737974 Reorder the terms: -2 + t = -1.457737974 Solving -2 + t = -1.457737974 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = -1.457737974 + 2 Combine like terms: -2 + 2 = 0 0 + t = -1.457737974 + 2 t = -1.457737974 + 2 Combine like terms: -1.457737974 + 2 = 0.542262026 t = 0.542262026 Simplifying t = 0.542262026Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.457737974, 0.542262026}Solution
t = {3.457737974, 0.542262026}
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