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Simplifying t2 + -10t + -400 = 0 Reorder the terms: -400 + -10t + t2 = 0 Solving -400 + -10t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '400' to each side of the equation. -400 + -10t + 400 + t2 = 0 + 400 Reorder the terms: -400 + 400 + -10t + t2 = 0 + 400 Combine like terms: -400 + 400 = 0 0 + -10t + t2 = 0 + 400 -10t + t2 = 0 + 400 Combine like terms: 0 + 400 = 400 -10t + t2 = 400 The t term is -10t. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10t + 25 + t2 = 400 + 25 Reorder the terms: 25 + -10t + t2 = 400 + 25 Combine like terms: 400 + 25 = 425 25 + -10t + t2 = 425 Factor a perfect square on the left side: (t + -5)(t + -5) = 425 Calculate the square root of the right side: 20.615528128 Break this problem into two subproblems by setting (t + -5) equal to 20.615528128 and -20.615528128.Subproblem 1
t + -5 = 20.615528128 Simplifying t + -5 = 20.615528128 Reorder the terms: -5 + t = 20.615528128 Solving -5 + t = 20.615528128 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = 20.615528128 + 5 Combine like terms: -5 + 5 = 0 0 + t = 20.615528128 + 5 t = 20.615528128 + 5 Combine like terms: 20.615528128 + 5 = 25.615528128 t = 25.615528128 Simplifying t = 25.615528128Subproblem 2
t + -5 = -20.615528128 Simplifying t + -5 = -20.615528128 Reorder the terms: -5 + t = -20.615528128 Solving -5 + t = -20.615528128 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = -20.615528128 + 5 Combine like terms: -5 + 5 = 0 0 + t = -20.615528128 + 5 t = -20.615528128 + 5 Combine like terms: -20.615528128 + 5 = -15.615528128 t = -15.615528128 Simplifying t = -15.615528128Solution
The solution to the problem is based on the solutions from the subproblems. t = {25.615528128, -15.615528128}
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