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Simplifying -16t2 + 64t + 45 = 0 Reorder the terms: 45 + 64t + -16t2 = 0 Solving 45 + 64t + -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'. -2.8125 + -4t + t2 = 0 Move the constant term to the right: Add '2.8125' to each side of the equation. -2.8125 + -4t + 2.8125 + t2 = 0 + 2.8125 Reorder the terms: -2.8125 + 2.8125 + -4t + t2 = 0 + 2.8125 Combine like terms: -2.8125 + 2.8125 = 0.0000 0.0000 + -4t + t2 = 0 + 2.8125 -4t + t2 = 0 + 2.8125 Combine like terms: 0 + 2.8125 = 2.8125 -4t + t2 = 2.8125 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 = 2.8125 + 4 Reorder the terms: 4 + -4t + t2 = 2.8125 + 4 Combine like terms: 2.8125 + 4 = 6.8125 4 + -4t + t2 = 6.8125 Factor a perfect square on the left side: (t + -2)(t + -2) = 6.8125 Calculate the square root of the right side: 2.610076627 Break this problem into two subproblems by setting (t + -2) equal to 2.610076627 and -2.610076627.Subproblem 1
t + -2 = 2.610076627 Simplifying t + -2 = 2.610076627 Reorder the terms: -2 + t = 2.610076627 Solving -2 + t = 2.610076627 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 = 2.610076627 + 2 Combine like terms: -2 + 2 = 0 0 + t = 2.610076627 + 2 t = 2.610076627 + 2 Combine like terms: 2.610076627 + 2 = 4.610076627 t = 4.610076627 Simplifying t = 4.610076627Subproblem 2
t + -2 = -2.610076627 Simplifying t + -2 = -2.610076627 Reorder the terms: -2 + t = -2.610076627 Solving -2 + t = -2.610076627 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 = -2.610076627 + 2 Combine like terms: -2 + 2 = 0 0 + t = -2.610076627 + 2 t = -2.610076627 + 2 Combine like terms: -2.610076627 + 2 = -0.610076627 t = -0.610076627 Simplifying t = -0.610076627Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.610076627, -0.610076627}
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