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Simplifying 0 = -16t2 + 64t + 90 Reorder the terms: 0 = 90 + 64t + -16t2 Solving 0 = 90 + 64t + -16t2 Solving for variable 't'. Combine like terms: 0 + -90 = -90 -90 + -64t + 16t2 = 90 + 64t + -16t2 + -90 + -64t + 16t2 Reorder the terms: -90 + -64t + 16t2 = 90 + -90 + 64t + -64t + -16t2 + 16t2 Combine like terms: 90 + -90 = 0 -90 + -64t + 16t2 = 0 + 64t + -64t + -16t2 + 16t2 -90 + -64t + 16t2 = 64t + -64t + -16t2 + 16t2 Combine like terms: 64t + -64t = 0 -90 + -64t + 16t2 = 0 + -16t2 + 16t2 -90 + -64t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -90 + -64t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-45 + -32t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-45 + -32t + 8t2)' equal to zero and attempt to solve: Simplifying -45 + -32t + 8t2 = 0 Solving -45 + -32t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -5.625 + -4t + t2 = 0 Move the constant term to the right: Add '5.625' to each side of the equation. -5.625 + -4t + 5.625 + t2 = 0 + 5.625 Reorder the terms: -5.625 + 5.625 + -4t + t2 = 0 + 5.625 Combine like terms: -5.625 + 5.625 = 0.000 0.000 + -4t + t2 = 0 + 5.625 -4t + t2 = 0 + 5.625 Combine like terms: 0 + 5.625 = 5.625 -4t + t2 = 5.625 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 = 5.625 + 4 Reorder the terms: 4 + -4t + t2 = 5.625 + 4 Combine like terms: 5.625 + 4 = 9.625 4 + -4t + t2 = 9.625 Factor a perfect square on the left side: (t + -2)(t + -2) = 9.625 Calculate the square root of the right side: 3.102418411 Break this problem into two subproblems by setting (t + -2) equal to 3.102418411 and -3.102418411.Subproblem 1
t + -2 = 3.102418411 Simplifying t + -2 = 3.102418411 Reorder the terms: -2 + t = 3.102418411 Solving -2 + t = 3.102418411 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 = 3.102418411 + 2 Combine like terms: -2 + 2 = 0 0 + t = 3.102418411 + 2 t = 3.102418411 + 2 Combine like terms: 3.102418411 + 2 = 5.102418411 t = 5.102418411 Simplifying t = 5.102418411Subproblem 2
t + -2 = -3.102418411 Simplifying t + -2 = -3.102418411 Reorder the terms: -2 + t = -3.102418411 Solving -2 + t = -3.102418411 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 = -3.102418411 + 2 Combine like terms: -2 + 2 = 0 0 + t = -3.102418411 + 2 t = -3.102418411 + 2 Combine like terms: -3.102418411 + 2 = -1.102418411 t = -1.102418411 Simplifying t = -1.102418411Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.102418411, -1.102418411}Solution
t = {5.102418411, -1.102418411}
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