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Simplifying -16t2 + 50t + 32 = 0 Reorder the terms: 32 + 50t + -16t2 = 0 Solving 32 + 50t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(16 + 25t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(16 + 25t + -8t2)' equal to zero and attempt to solve: Simplifying 16 + 25t + -8t2 = 0 Solving 16 + 25t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -2 + -3.125t + t2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -3.125t + 2 + t2 = 0 + 2 Reorder the terms: -2 + 2 + -3.125t + t2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3.125t + t2 = 0 + 2 -3.125t + t2 = 0 + 2 Combine like terms: 0 + 2 = 2 -3.125t + t2 = 2 The t term is -3.125t. Take half its coefficient (-1.5625). Square it (2.44140625) and add it to both sides. Add '2.44140625' to each side of the equation. -3.125t + 2.44140625 + t2 = 2 + 2.44140625 Reorder the terms: 2.44140625 + -3.125t + t2 = 2 + 2.44140625 Combine like terms: 2 + 2.44140625 = 4.44140625 2.44140625 + -3.125t + t2 = 4.44140625 Factor a perfect square on the left side: (t + -1.5625)(t + -1.5625) = 4.44140625 Calculate the square root of the right side: 2.107464413 Break this problem into two subproblems by setting (t + -1.5625) equal to 2.107464413 and -2.107464413.Subproblem 1
t + -1.5625 = 2.107464413 Simplifying t + -1.5625 = 2.107464413 Reorder the terms: -1.5625 + t = 2.107464413 Solving -1.5625 + t = 2.107464413 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + t = 2.107464413 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + t = 2.107464413 + 1.5625 t = 2.107464413 + 1.5625 Combine like terms: 2.107464413 + 1.5625 = 3.669964413 t = 3.669964413 Simplifying t = 3.669964413Subproblem 2
t + -1.5625 = -2.107464413 Simplifying t + -1.5625 = -2.107464413 Reorder the terms: -1.5625 + t = -2.107464413 Solving -1.5625 + t = -2.107464413 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + t = -2.107464413 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + t = -2.107464413 + 1.5625 t = -2.107464413 + 1.5625 Combine like terms: -2.107464413 + 1.5625 = -0.544964413 t = -0.544964413 Simplifying t = -0.544964413Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.669964413, -0.544964413}Solution
t = {3.669964413, -0.544964413}
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