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Simplifying 20t2 + 18t + -5 = 0 Reorder the terms: -5 + 18t + 20t2 = 0 Solving -5 + 18t + 20t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -0.25 + 0.9t + t2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + 0.9t + 0.25 + t2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + 0.9t + t2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + 0.9t + t2 = 0 + 0.25 0.9t + t2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 0.9t + t2 = 0.25 The t term is 0.9t. Take half its coefficient (0.45). Square it (0.2025) and add it to both sides. Add '0.2025' to each side of the equation. 0.9t + 0.2025 + t2 = 0.25 + 0.2025 Reorder the terms: 0.2025 + 0.9t + t2 = 0.25 + 0.2025 Combine like terms: 0.25 + 0.2025 = 0.4525 0.2025 + 0.9t + t2 = 0.4525 Factor a perfect square on the left side: (t + 0.45)(t + 0.45) = 0.4525 Calculate the square root of the right side: 0.672681202 Break this problem into two subproblems by setting (t + 0.45) equal to 0.672681202 and -0.672681202.Subproblem 1
t + 0.45 = 0.672681202 Simplifying t + 0.45 = 0.672681202 Reorder the terms: 0.45 + t = 0.672681202 Solving 0.45 + t = 0.672681202 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.45' to each side of the equation. 0.45 + -0.45 + t = 0.672681202 + -0.45 Combine like terms: 0.45 + -0.45 = 0.00 0.00 + t = 0.672681202 + -0.45 t = 0.672681202 + -0.45 Combine like terms: 0.672681202 + -0.45 = 0.222681202 t = 0.222681202 Simplifying t = 0.222681202Subproblem 2
t + 0.45 = -0.672681202 Simplifying t + 0.45 = -0.672681202 Reorder the terms: 0.45 + t = -0.672681202 Solving 0.45 + t = -0.672681202 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.45' to each side of the equation. 0.45 + -0.45 + t = -0.672681202 + -0.45 Combine like terms: 0.45 + -0.45 = 0.00 0.00 + t = -0.672681202 + -0.45 t = -0.672681202 + -0.45 Combine like terms: -0.672681202 + -0.45 = -1.122681202 t = -1.122681202 Simplifying t = -1.122681202Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.222681202, -1.122681202}
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