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Simplifying 159 = 16t2 + 32t Reorder the terms: 159 = 32t + 16t2 Solving 159 = 32t + 16t2 Solving for variable 't'. Reorder the terms: 159 + -32t + -16t2 = 32t + -32t + 16t2 + -16t2 Combine like terms: 32t + -32t = 0 159 + -32t + -16t2 = 0 + 16t2 + -16t2 159 + -32t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 159 + -32t + -16t2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -9.9375 + 2t + t2 = 0 Move the constant term to the right: Add '9.9375' to each side of the equation. -9.9375 + 2t + 9.9375 + t2 = 0 + 9.9375 Reorder the terms: -9.9375 + 9.9375 + 2t + t2 = 0 + 9.9375 Combine like terms: -9.9375 + 9.9375 = 0.0000 0.0000 + 2t + t2 = 0 + 9.9375 2t + t2 = 0 + 9.9375 Combine like terms: 0 + 9.9375 = 9.9375 2t + t2 = 9.9375 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 = 9.9375 + 1 Reorder the terms: 1 + 2t + t2 = 9.9375 + 1 Combine like terms: 9.9375 + 1 = 10.9375 1 + 2t + t2 = 10.9375 Factor a perfect square on the left side: (t + 1)(t + 1) = 10.9375 Calculate the square root of the right side: 3.307189139 Break this problem into two subproblems by setting (t + 1) equal to 3.307189139 and -3.307189139.Subproblem 1
t + 1 = 3.307189139 Simplifying t + 1 = 3.307189139 Reorder the terms: 1 + t = 3.307189139 Solving 1 + t = 3.307189139 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 = 3.307189139 + -1 Combine like terms: 1 + -1 = 0 0 + t = 3.307189139 + -1 t = 3.307189139 + -1 Combine like terms: 3.307189139 + -1 = 2.307189139 t = 2.307189139 Simplifying t = 2.307189139Subproblem 2
t + 1 = -3.307189139 Simplifying t + 1 = -3.307189139 Reorder the terms: 1 + t = -3.307189139 Solving 1 + t = -3.307189139 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 = -3.307189139 + -1 Combine like terms: 1 + -1 = 0 0 + t = -3.307189139 + -1 t = -3.307189139 + -1 Combine like terms: -3.307189139 + -1 = -4.307189139 t = -4.307189139 Simplifying t = -4.307189139Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.307189139, -4.307189139}
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