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Simplifying -16t2 + -13t + 150 = 0 Reorder the terms: 150 + -13t + -16t2 = 0 Solving 150 + -13t + -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'. -9.375 + 0.8125t + t2 = 0 Move the constant term to the right: Add '9.375' to each side of the equation. -9.375 + 0.8125t + 9.375 + t2 = 0 + 9.375 Reorder the terms: -9.375 + 9.375 + 0.8125t + t2 = 0 + 9.375 Combine like terms: -9.375 + 9.375 = 0.000 0.000 + 0.8125t + t2 = 0 + 9.375 0.8125t + t2 = 0 + 9.375 Combine like terms: 0 + 9.375 = 9.375 0.8125t + t2 = 9.375 The t term is 0.8125t. Take half its coefficient (0.40625). Square it (0.1650390625) and add it to both sides. Add '0.1650390625' to each side of the equation. 0.8125t + 0.1650390625 + t2 = 9.375 + 0.1650390625 Reorder the terms: 0.1650390625 + 0.8125t + t2 = 9.375 + 0.1650390625 Combine like terms: 9.375 + 0.1650390625 = 9.5400390625 0.1650390625 + 0.8125t + t2 = 9.5400390625 Factor a perfect square on the left side: (t + 0.40625)(t + 0.40625) = 9.5400390625 Calculate the square root of the right side: 3.088695366 Break this problem into two subproblems by setting (t + 0.40625) equal to 3.088695366 and -3.088695366.Subproblem 1
t + 0.40625 = 3.088695366 Simplifying t + 0.40625 = 3.088695366 Reorder the terms: 0.40625 + t = 3.088695366 Solving 0.40625 + t = 3.088695366 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.40625' to each side of the equation. 0.40625 + -0.40625 + t = 3.088695366 + -0.40625 Combine like terms: 0.40625 + -0.40625 = 0.00000 0.00000 + t = 3.088695366 + -0.40625 t = 3.088695366 + -0.40625 Combine like terms: 3.088695366 + -0.40625 = 2.682445366 t = 2.682445366 Simplifying t = 2.682445366Subproblem 2
t + 0.40625 = -3.088695366 Simplifying t + 0.40625 = -3.088695366 Reorder the terms: 0.40625 + t = -3.088695366 Solving 0.40625 + t = -3.088695366 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.40625' to each side of the equation. 0.40625 + -0.40625 + t = -3.088695366 + -0.40625 Combine like terms: 0.40625 + -0.40625 = 0.00000 0.00000 + t = -3.088695366 + -0.40625 t = -3.088695366 + -0.40625 Combine like terms: -3.088695366 + -0.40625 = -3.494945366 t = -3.494945366 Simplifying t = -3.494945366Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.682445366, -3.494945366}
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