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Simplifying -16t2 + 48t + 137 = 0 Reorder the terms: 137 + 48t + -16t2 = 0 Solving 137 + 48t + -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'. -8.5625 + -3t + t2 = 0 Move the constant term to the right: Add '8.5625' to each side of the equation. -8.5625 + -3t + 8.5625 + t2 = 0 + 8.5625 Reorder the terms: -8.5625 + 8.5625 + -3t + t2 = 0 + 8.5625 Combine like terms: -8.5625 + 8.5625 = 0.0000 0.0000 + -3t + t2 = 0 + 8.5625 -3t + t2 = 0 + 8.5625 Combine like terms: 0 + 8.5625 = 8.5625 -3t + t2 = 8.5625 The t term is -3t. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3t + 2.25 + t2 = 8.5625 + 2.25 Reorder the terms: 2.25 + -3t + t2 = 8.5625 + 2.25 Combine like terms: 8.5625 + 2.25 = 10.8125 2.25 + -3t + t2 = 10.8125 Factor a perfect square on the left side: (t + -1.5)(t + -1.5) = 10.8125 Calculate the square root of the right side: 3.288236609 Break this problem into two subproblems by setting (t + -1.5) equal to 3.288236609 and -3.288236609.Subproblem 1
t + -1.5 = 3.288236609 Simplifying t + -1.5 = 3.288236609 Reorder the terms: -1.5 + t = 3.288236609 Solving -1.5 + t = 3.288236609 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + t = 3.288236609 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = 3.288236609 + 1.5 t = 3.288236609 + 1.5 Combine like terms: 3.288236609 + 1.5 = 4.788236609 t = 4.788236609 Simplifying t = 4.788236609Subproblem 2
t + -1.5 = -3.288236609 Simplifying t + -1.5 = -3.288236609 Reorder the terms: -1.5 + t = -3.288236609 Solving -1.5 + t = -3.288236609 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + t = -3.288236609 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = -3.288236609 + 1.5 t = -3.288236609 + 1.5 Combine like terms: -3.288236609 + 1.5 = -1.788236609 t = -1.788236609 Simplifying t = -1.788236609Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.788236609, -1.788236609}
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