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Simplifying -16t2 + 40t + -2.5 = 0 Reorder the terms: -2.5 + 40t + -16t2 = 0 Solving -2.5 + 40t + -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'. 0.15625 + -2.5t + t2 = 0 Move the constant term to the right: Add '-0.15625' to each side of the equation. 0.15625 + -2.5t + -0.15625 + t2 = 0 + -0.15625 Reorder the terms: 0.15625 + -0.15625 + -2.5t + t2 = 0 + -0.15625 Combine like terms: 0.15625 + -0.15625 = 0.00000 0.00000 + -2.5t + t2 = 0 + -0.15625 -2.5t + t2 = 0 + -0.15625 Combine like terms: 0 + -0.15625 = -0.15625 -2.5t + t2 = -0.15625 The t term is -2.5t. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5t + 1.5625 + t2 = -0.15625 + 1.5625 Reorder the terms: 1.5625 + -2.5t + t2 = -0.15625 + 1.5625 Combine like terms: -0.15625 + 1.5625 = 1.40625 1.5625 + -2.5t + t2 = 1.40625 Factor a perfect square on the left side: (t + -1.25)(t + -1.25) = 1.40625 Calculate the square root of the right side: 1.185854123 Break this problem into two subproblems by setting (t + -1.25) equal to 1.185854123 and -1.185854123.Subproblem 1
t + -1.25 = 1.185854123 Simplifying t + -1.25 = 1.185854123 Reorder the terms: -1.25 + t = 1.185854123 Solving -1.25 + t = 1.185854123 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + t = 1.185854123 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + t = 1.185854123 + 1.25 t = 1.185854123 + 1.25 Combine like terms: 1.185854123 + 1.25 = 2.435854123 t = 2.435854123 Simplifying t = 2.435854123Subproblem 2
t + -1.25 = -1.185854123 Simplifying t + -1.25 = -1.185854123 Reorder the terms: -1.25 + t = -1.185854123 Solving -1.25 + t = -1.185854123 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + t = -1.185854123 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + t = -1.185854123 + 1.25 t = -1.185854123 + 1.25 Combine like terms: -1.185854123 + 1.25 = 0.064145877 t = 0.064145877 Simplifying t = 0.064145877Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.435854123, 0.064145877}
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