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Simplifying 5 + 25t + -10t2 = 0 Solving 5 + 25t + -10t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '5'. 5(1 + 5t + -2t2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(1 + 5t + -2t2)' equal to zero and attempt to solve: Simplifying 1 + 5t + -2t2 = 0 Solving 1 + 5t + -2t2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -0.5 + -2.5t + t2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -2.5t + 0.5 + t2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -2.5t + t2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -2.5t + t2 = 0 + 0.5 -2.5t + t2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -2.5t + t2 = 0.5 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 = 0.5 + 1.5625 Reorder the terms: 1.5625 + -2.5t + t2 = 0.5 + 1.5625 Combine like terms: 0.5 + 1.5625 = 2.0625 1.5625 + -2.5t + t2 = 2.0625 Factor a perfect square on the left side: (t + -1.25)(t + -1.25) = 2.0625 Calculate the square root of the right side: 1.436140662 Break this problem into two subproblems by setting (t + -1.25) equal to 1.436140662 and -1.436140662.Subproblem 1
t + -1.25 = 1.436140662 Simplifying t + -1.25 = 1.436140662 Reorder the terms: -1.25 + t = 1.436140662 Solving -1.25 + t = 1.436140662 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 = 1.436140662 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + t = 1.436140662 + 1.25 t = 1.436140662 + 1.25 Combine like terms: 1.436140662 + 1.25 = 2.686140662 t = 2.686140662 Simplifying t = 2.686140662Subproblem 2
t + -1.25 = -1.436140662 Simplifying t + -1.25 = -1.436140662 Reorder the terms: -1.25 + t = -1.436140662 Solving -1.25 + t = -1.436140662 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 = -1.436140662 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + t = -1.436140662 + 1.25 t = -1.436140662 + 1.25 Combine like terms: -1.436140662 + 1.25 = -0.186140662 t = -0.186140662 Simplifying t = -0.186140662Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.686140662, -0.186140662}Solution
t = {2.686140662, -0.186140662}
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