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Simplifying 0.01t2 + 0.5t + -14 = 0 Reorder the terms: -14 + 0.5t + 0.01t2 = 0 Solving -14 + 0.5t + 0.01t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 0.01 the coefficient of the squared term: Divide each side by '0.01'. -1400 + 50t + t2 = 0 Move the constant term to the right: Add '1400' to each side of the equation. -1400 + 50t + 1400 + t2 = 0 + 1400 Reorder the terms: -1400 + 1400 + 50t + t2 = 0 + 1400 Combine like terms: -1400 + 1400 = 0 0 + 50t + t2 = 0 + 1400 50t + t2 = 0 + 1400 Combine like terms: 0 + 1400 = 1400 50t + t2 = 1400 The t term is 50t. Take half its coefficient (25). Square it (625) and add it to both sides. Add '625' to each side of the equation. 50t + 625 + t2 = 1400 + 625 Reorder the terms: 625 + 50t + t2 = 1400 + 625 Combine like terms: 1400 + 625 = 2025 625 + 50t + t2 = 2025 Factor a perfect square on the left side: (t + 25)(t + 25) = 2025 Calculate the square root of the right side: 45 Break this problem into two subproblems by setting (t + 25) equal to 45 and -45.Subproblem 1
t + 25 = 45 Simplifying t + 25 = 45 Reorder the terms: 25 + t = 45 Solving 25 + t = 45 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + t = 45 + -25 Combine like terms: 25 + -25 = 0 0 + t = 45 + -25 t = 45 + -25 Combine like terms: 45 + -25 = 20 t = 20 Simplifying t = 20Subproblem 2
t + 25 = -45 Simplifying t + 25 = -45 Reorder the terms: 25 + t = -45 Solving 25 + t = -45 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + t = -45 + -25 Combine like terms: 25 + -25 = 0 0 + t = -45 + -25 t = -45 + -25 Combine like terms: -45 + -25 = -70 t = -70 Simplifying t = -70Solution
The solution to the problem is based on the solutions from the subproblems. t = {20, -70}
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