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Simplifying 16t2 + -110.5t + 2.98 = 0 Reorder the terms: 2.98 + -110.5t + 16t2 = 0 Solving 2.98 + -110.5t + 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'. 0.18625 + -6.90625t + t2 = 0 Move the constant term to the right: Add '-0.18625' to each side of the equation. 0.18625 + -6.90625t + -0.18625 + t2 = 0 + -0.18625 Reorder the terms: 0.18625 + -0.18625 + -6.90625t + t2 = 0 + -0.18625 Combine like terms: 0.18625 + -0.18625 = 0.00000 0.00000 + -6.90625t + t2 = 0 + -0.18625 -6.90625t + t2 = 0 + -0.18625 Combine like terms: 0 + -0.18625 = -0.18625 -6.90625t + t2 = -0.18625 The t term is -6.90625t. Take half its coefficient (-3.453125). Square it (11.92407227) and add it to both sides. Add '11.92407227' to each side of the equation. -6.90625t + 11.92407227 + t2 = -0.18625 + 11.92407227 Reorder the terms: 11.92407227 + -6.90625t + t2 = -0.18625 + 11.92407227 Combine like terms: -0.18625 + 11.92407227 = 11.73782227 11.92407227 + -6.90625t + t2 = 11.73782227 Factor a perfect square on the left side: (t + -3.453125)(t + -3.453125) = 11.73782227 Calculate the square root of the right side: 3.426050535 Break this problem into two subproblems by setting (t + -3.453125) equal to 3.426050535 and -3.426050535.Subproblem 1
t + -3.453125 = 3.426050535 Simplifying t + -3.453125 = 3.426050535 Reorder the terms: -3.453125 + t = 3.426050535 Solving -3.453125 + t = 3.426050535 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.453125' to each side of the equation. -3.453125 + 3.453125 + t = 3.426050535 + 3.453125 Combine like terms: -3.453125 + 3.453125 = 0.000000 0.000000 + t = 3.426050535 + 3.453125 t = 3.426050535 + 3.453125 Combine like terms: 3.426050535 + 3.453125 = 6.879175535 t = 6.879175535 Simplifying t = 6.879175535Subproblem 2
t + -3.453125 = -3.426050535 Simplifying t + -3.453125 = -3.426050535 Reorder the terms: -3.453125 + t = -3.426050535 Solving -3.453125 + t = -3.426050535 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.453125' to each side of the equation. -3.453125 + 3.453125 + t = -3.426050535 + 3.453125 Combine like terms: -3.453125 + 3.453125 = 0.000000 0.000000 + t = -3.426050535 + 3.453125 t = -3.426050535 + 3.453125 Combine like terms: -3.426050535 + 3.453125 = 0.027074465 t = 0.027074465 Simplifying t = 0.027074465Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.879175535, 0.027074465}
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