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Simplifying -16t2 + 50t + 4.5 = 3.1931 Reorder the terms: 4.5 + 50t + -16t2 = 3.1931 Solving 4.5 + 50t + -16t2 = 3.1931 Solving for variable 't'. Reorder the terms: 4.5 + -3.1931 + 50t + -16t2 = 3.1931 + -3.1931 Combine like terms: 4.5 + -3.1931 = 1.3069 1.3069 + 50t + -16t2 = 3.1931 + -3.1931 Combine like terms: 3.1931 + -3.1931 = 0.0000 1.3069 + 50t + -16t2 = 0.0000 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.08168125 + -3.125t + t2 = 0.0000 Move the constant term to the right: Add '0.08168125' to each side of the equation. -0.08168125 + -3.125t + 0.08168125 + t2 = 0.0000 + 0.08168125 Reorder the terms: -0.08168125 + 0.08168125 + -3.125t + t2 = 0.0000 + 0.08168125 Combine like terms: -0.08168125 + 0.08168125 = 0.00000000 0.00000000 + -3.125t + t2 = 0.0000 + 0.08168125 -3.125t + t2 = 0.0000 + 0.08168125 Combine like terms: 0.0000 + 0.08168125 = 0.08168125 -3.125t + t2 = 0.08168125 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 = 0.08168125 + 2.44140625 Reorder the terms: 2.44140625 + -3.125t + t2 = 0.08168125 + 2.44140625 Combine like terms: 0.08168125 + 2.44140625 = 2.5230875 2.44140625 + -3.125t + t2 = 2.5230875 Factor a perfect square on the left side: (t + -1.5625)(t + -1.5625) = 2.5230875 Calculate the square root of the right side: 1.58842296 Break this problem into two subproblems by setting (t + -1.5625) equal to 1.58842296 and -1.58842296.Subproblem 1
t + -1.5625 = 1.58842296 Simplifying t + -1.5625 = 1.58842296 Reorder the terms: -1.5625 + t = 1.58842296 Solving -1.5625 + t = 1.58842296 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 = 1.58842296 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + t = 1.58842296 + 1.5625 t = 1.58842296 + 1.5625 Combine like terms: 1.58842296 + 1.5625 = 3.15092296 t = 3.15092296 Simplifying t = 3.15092296Subproblem 2
t + -1.5625 = -1.58842296 Simplifying t + -1.5625 = -1.58842296 Reorder the terms: -1.5625 + t = -1.58842296 Solving -1.5625 + t = -1.58842296 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 = -1.58842296 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + t = -1.58842296 + 1.5625 t = -1.58842296 + 1.5625 Combine like terms: -1.58842296 + 1.5625 = -0.02592296 t = -0.02592296 Simplifying t = -0.02592296Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.15092296, -0.02592296}
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