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Simplifying -16t2 + 40t + 20 = 0 Reorder the terms: 20 + 40t + -16t2 = 0 Solving 20 + 40t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(5 + 10t + -4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(5 + 10t + -4t2)' equal to zero and attempt to solve: Simplifying 5 + 10t + -4t2 = 0 Solving 5 + 10t + -4t2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -1.25 + -2.5t + t2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -2.5t + 1.25 + t2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -2.5t + t2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -2.5t + t2 = 0 + 1.25 -2.5t + t2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -2.5t + t2 = 1.25 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 = 1.25 + 1.5625 Reorder the terms: 1.5625 + -2.5t + t2 = 1.25 + 1.5625 Combine like terms: 1.25 + 1.5625 = 2.8125 1.5625 + -2.5t + t2 = 2.8125 Factor a perfect square on the left side: (t + -1.25)(t + -1.25) = 2.8125 Calculate the square root of the right side: 1.677050983 Break this problem into two subproblems by setting (t + -1.25) equal to 1.677050983 and -1.677050983.Subproblem 1
t + -1.25 = 1.677050983 Simplifying t + -1.25 = 1.677050983 Reorder the terms: -1.25 + t = 1.677050983 Solving -1.25 + t = 1.677050983 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 = 1.677050983 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + t = 1.677050983 + 1.25 t = 1.677050983 + 1.25 Combine like terms: 1.677050983 + 1.25 = 2.927050983 t = 2.927050983 Simplifying t = 2.927050983Subproblem 2
t + -1.25 = -1.677050983 Simplifying t + -1.25 = -1.677050983 Reorder the terms: -1.25 + t = -1.677050983 Solving -1.25 + t = -1.677050983 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 = -1.677050983 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + t = -1.677050983 + 1.25 t = -1.677050983 + 1.25 Combine like terms: -1.677050983 + 1.25 = -0.427050983 t = -0.427050983 Simplifying t = -0.427050983Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.927050983, -0.427050983}Solution
t = {2.927050983, -0.427050983}
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