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Simplifying -16t2 + 152t + 361 = 0 Reorder the terms: 361 + 152t + -16t2 = 0 Solving 361 + 152t + -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'. -22.5625 + -9.5t + t2 = 0 Move the constant term to the right: Add '22.5625' to each side of the equation. -22.5625 + -9.5t + 22.5625 + t2 = 0 + 22.5625 Reorder the terms: -22.5625 + 22.5625 + -9.5t + t2 = 0 + 22.5625 Combine like terms: -22.5625 + 22.5625 = 0.0000 0.0000 + -9.5t + t2 = 0 + 22.5625 -9.5t + t2 = 0 + 22.5625 Combine like terms: 0 + 22.5625 = 22.5625 -9.5t + t2 = 22.5625 The t term is -9.5t. Take half its coefficient (-4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. -9.5t + 22.5625 + t2 = 22.5625 + 22.5625 Reorder the terms: 22.5625 + -9.5t + t2 = 22.5625 + 22.5625 Combine like terms: 22.5625 + 22.5625 = 45.125 22.5625 + -9.5t + t2 = 45.125 Factor a perfect square on the left side: (t + -4.75)(t + -4.75) = 45.125 Calculate the square root of the right side: 6.717514421 Break this problem into two subproblems by setting (t + -4.75) equal to 6.717514421 and -6.717514421.Subproblem 1
t + -4.75 = 6.717514421 Simplifying t + -4.75 = 6.717514421 Reorder the terms: -4.75 + t = 6.717514421 Solving -4.75 + t = 6.717514421 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + t = 6.717514421 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + t = 6.717514421 + 4.75 t = 6.717514421 + 4.75 Combine like terms: 6.717514421 + 4.75 = 11.467514421 t = 11.467514421 Simplifying t = 11.467514421Subproblem 2
t + -4.75 = -6.717514421 Simplifying t + -4.75 = -6.717514421 Reorder the terms: -4.75 + t = -6.717514421 Solving -4.75 + t = -6.717514421 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + t = -6.717514421 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + t = -6.717514421 + 4.75 t = -6.717514421 + 4.75 Combine like terms: -6.717514421 + 4.75 = -1.967514421 t = -1.967514421 Simplifying t = -1.967514421Solution
The solution to the problem is based on the solutions from the subproblems. t = {11.467514421, -1.967514421}
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