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Simplifying t2 + 30t + -200 = 0 Reorder the terms: -200 + 30t + t2 = 0 Solving -200 + 30t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '200' to each side of the equation. -200 + 30t + 200 + t2 = 0 + 200 Reorder the terms: -200 + 200 + 30t + t2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + 30t + t2 = 0 + 200 30t + t2 = 0 + 200 Combine like terms: 0 + 200 = 200 30t + t2 = 200 The t term is 30t. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30t + 225 + t2 = 200 + 225 Reorder the terms: 225 + 30t + t2 = 200 + 225 Combine like terms: 200 + 225 = 425 225 + 30t + t2 = 425 Factor a perfect square on the left side: (t + 15)(t + 15) = 425 Calculate the square root of the right side: 20.615528128 Break this problem into two subproblems by setting (t + 15) equal to 20.615528128 and -20.615528128.Subproblem 1
t + 15 = 20.615528128 Simplifying t + 15 = 20.615528128 Reorder the terms: 15 + t = 20.615528128 Solving 15 + t = 20.615528128 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + t = 20.615528128 + -15 Combine like terms: 15 + -15 = 0 0 + t = 20.615528128 + -15 t = 20.615528128 + -15 Combine like terms: 20.615528128 + -15 = 5.615528128 t = 5.615528128 Simplifying t = 5.615528128Subproblem 2
t + 15 = -20.615528128 Simplifying t + 15 = -20.615528128 Reorder the terms: 15 + t = -20.615528128 Solving 15 + t = -20.615528128 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + t = -20.615528128 + -15 Combine like terms: 15 + -15 = 0 0 + t = -20.615528128 + -15 t = -20.615528128 + -15 Combine like terms: -20.615528128 + -15 = -35.615528128 t = -35.615528128 Simplifying t = -35.615528128Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.615528128, -35.615528128}
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