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Simplifying -2t2 + 10t + 25 = 0 Reorder the terms: 25 + 10t + -2t2 = 0 Solving 25 + 10t + -2t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -12.5 + -5t + t2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + -5t + 12.5 + t2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + -5t + t2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + -5t + t2 = 0 + 12.5 -5t + t2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 -5t + t2 = 12.5 The t term is -5t. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5t + 6.25 + t2 = 12.5 + 6.25 Reorder the terms: 6.25 + -5t + t2 = 12.5 + 6.25 Combine like terms: 12.5 + 6.25 = 18.75 6.25 + -5t + t2 = 18.75 Factor a perfect square on the left side: (t + -2.5)(t + -2.5) = 18.75 Calculate the square root of the right side: 4.330127019 Break this problem into two subproblems by setting (t + -2.5) equal to 4.330127019 and -4.330127019.Subproblem 1
t + -2.5 = 4.330127019 Simplifying t + -2.5 = 4.330127019 Reorder the terms: -2.5 + t = 4.330127019 Solving -2.5 + t = 4.330127019 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = 4.330127019 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = 4.330127019 + 2.5 t = 4.330127019 + 2.5 Combine like terms: 4.330127019 + 2.5 = 6.830127019 t = 6.830127019 Simplifying t = 6.830127019Subproblem 2
t + -2.5 = -4.330127019 Simplifying t + -2.5 = -4.330127019 Reorder the terms: -2.5 + t = -4.330127019 Solving -2.5 + t = -4.330127019 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = -4.330127019 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = -4.330127019 + 2.5 t = -4.330127019 + 2.5 Combine like terms: -4.330127019 + 2.5 = -1.830127019 t = -1.830127019 Simplifying t = -1.830127019Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.830127019, -1.830127019}
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