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Simplifying -16t2 + 32t + 45 = 0 Reorder the terms: 45 + 32t + -16t2 = 0 Solving 45 + 32t + -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 + -2t + t2 = 0 Move the constant term to the right: Add '2.8125' to each side of the equation. -2.8125 + -2t + 2.8125 + t2 = 0 + 2.8125 Reorder the terms: -2.8125 + 2.8125 + -2t + t2 = 0 + 2.8125 Combine like terms: -2.8125 + 2.8125 = 0.0000 0.0000 + -2t + t2 = 0 + 2.8125 -2t + t2 = 0 + 2.8125 Combine like terms: 0 + 2.8125 = 2.8125 -2t + t2 = 2.8125 The t term is -2t. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2t + 1 + t2 = 2.8125 + 1 Reorder the terms: 1 + -2t + t2 = 2.8125 + 1 Combine like terms: 2.8125 + 1 = 3.8125 1 + -2t + t2 = 3.8125 Factor a perfect square on the left side: (t + -1)(t + -1) = 3.8125 Calculate the square root of the right side: 1.952562419 Break this problem into two subproblems by setting (t + -1) equal to 1.952562419 and -1.952562419.Subproblem 1
t + -1 = 1.952562419 Simplifying t + -1 = 1.952562419 Reorder the terms: -1 + t = 1.952562419 Solving -1 + t = 1.952562419 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + t = 1.952562419 + 1 Combine like terms: -1 + 1 = 0 0 + t = 1.952562419 + 1 t = 1.952562419 + 1 Combine like terms: 1.952562419 + 1 = 2.952562419 t = 2.952562419 Simplifying t = 2.952562419Subproblem 2
t + -1 = -1.952562419 Simplifying t + -1 = -1.952562419 Reorder the terms: -1 + t = -1.952562419 Solving -1 + t = -1.952562419 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + t = -1.952562419 + 1 Combine like terms: -1 + 1 = 0 0 + t = -1.952562419 + 1 t = -1.952562419 + 1 Combine like terms: -1.952562419 + 1 = -0.952562419 t = -0.952562419 Simplifying t = -0.952562419Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.952562419, -0.952562419}
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