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Simplifying -16t2 + 50t + 8 = 0 Reorder the terms: 8 + 50t + -16t2 = 0 Solving 8 + 50t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(4 + 25t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + 25t + -8t2)' equal to zero and attempt to solve: Simplifying 4 + 25t + -8t2 = 0 Solving 4 + 25t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.5 + -3.125t + t2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -3.125t + 0.5 + t2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -3.125t + t2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -3.125t + t2 = 0 + 0.5 -3.125t + t2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -3.125t + t2 = 0.5 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 = 0.5 + 2.44140625 Reorder the terms: 2.44140625 + -3.125t + t2 = 0.5 + 2.44140625 Combine like terms: 0.5 + 2.44140625 = 2.94140625 2.44140625 + -3.125t + t2 = 2.94140625 Factor a perfect square on the left side: (t + -1.5625)(t + -1.5625) = 2.94140625 Calculate the square root of the right side: 1.715052842 Break this problem into two subproblems by setting (t + -1.5625) equal to 1.715052842 and -1.715052842.Subproblem 1
t + -1.5625 = 1.715052842 Simplifying t + -1.5625 = 1.715052842 Reorder the terms: -1.5625 + t = 1.715052842 Solving -1.5625 + t = 1.715052842 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 = 1.715052842 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + t = 1.715052842 + 1.5625 t = 1.715052842 + 1.5625 Combine like terms: 1.715052842 + 1.5625 = 3.277552842 t = 3.277552842 Simplifying t = 3.277552842Subproblem 2
t + -1.5625 = -1.715052842 Simplifying t + -1.5625 = -1.715052842 Reorder the terms: -1.5625 + t = -1.715052842 Solving -1.5625 + t = -1.715052842 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 = -1.715052842 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + t = -1.715052842 + 1.5625 t = -1.715052842 + 1.5625 Combine like terms: -1.715052842 + 1.5625 = -0.152552842 t = -0.152552842 Simplifying t = -0.152552842Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.277552842, -0.152552842}Solution
t = {3.277552842, -0.152552842}
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