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Simplifying 16t2 + -180t = 296 Reorder the terms: -180t + 16t2 = 296 Solving -180t + 16t2 = 296 Solving for variable 't'. Reorder the terms: -296 + -180t + 16t2 = 296 + -296 Combine like terms: 296 + -296 = 0 -296 + -180t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-74 + -45t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-74 + -45t + 4t2)' equal to zero and attempt to solve: Simplifying -74 + -45t + 4t2 = 0 Solving -74 + -45t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -18.5 + -11.25t + t2 = 0 Move the constant term to the right: Add '18.5' to each side of the equation. -18.5 + -11.25t + 18.5 + t2 = 0 + 18.5 Reorder the terms: -18.5 + 18.5 + -11.25t + t2 = 0 + 18.5 Combine like terms: -18.5 + 18.5 = 0.0 0.0 + -11.25t + t2 = 0 + 18.5 -11.25t + t2 = 0 + 18.5 Combine like terms: 0 + 18.5 = 18.5 -11.25t + t2 = 18.5 The t term is -11.25t. Take half its coefficient (-5.625). Square it (31.640625) and add it to both sides. Add '31.640625' to each side of the equation. -11.25t + 31.640625 + t2 = 18.5 + 31.640625 Reorder the terms: 31.640625 + -11.25t + t2 = 18.5 + 31.640625 Combine like terms: 18.5 + 31.640625 = 50.140625 31.640625 + -11.25t + t2 = 50.140625 Factor a perfect square on the left side: (t + -5.625)(t + -5.625) = 50.140625 Calculate the square root of the right side: 7.081004519 Break this problem into two subproblems by setting (t + -5.625) equal to 7.081004519 and -7.081004519.Subproblem 1
t + -5.625 = 7.081004519 Simplifying t + -5.625 = 7.081004519 Reorder the terms: -5.625 + t = 7.081004519 Solving -5.625 + t = 7.081004519 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.625' to each side of the equation. -5.625 + 5.625 + t = 7.081004519 + 5.625 Combine like terms: -5.625 + 5.625 = 0.000 0.000 + t = 7.081004519 + 5.625 t = 7.081004519 + 5.625 Combine like terms: 7.081004519 + 5.625 = 12.706004519 t = 12.706004519 Simplifying t = 12.706004519Subproblem 2
t + -5.625 = -7.081004519 Simplifying t + -5.625 = -7.081004519 Reorder the terms: -5.625 + t = -7.081004519 Solving -5.625 + t = -7.081004519 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.625' to each side of the equation. -5.625 + 5.625 + t = -7.081004519 + 5.625 Combine like terms: -5.625 + 5.625 = 0.000 0.000 + t = -7.081004519 + 5.625 t = -7.081004519 + 5.625 Combine like terms: -7.081004519 + 5.625 = -1.456004519 t = -1.456004519 Simplifying t = -1.456004519Solution
The solution to the problem is based on the solutions from the subproblems. t = {12.706004519, -1.456004519}Solution
t = {12.706004519, -1.456004519}
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