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Simplifying t2 + -2t + -8.5 = 0 Reorder the terms: -8.5 + -2t + t2 = 0 Solving -8.5 + -2t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '8.5' to each side of the equation. -8.5 + -2t + 8.5 + t2 = 0 + 8.5 Reorder the terms: -8.5 + 8.5 + -2t + t2 = 0 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + -2t + t2 = 0 + 8.5 -2t + t2 = 0 + 8.5 Combine like terms: 0 + 8.5 = 8.5 -2t + t2 = 8.5 The t term is -2t. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2t + 1 + t2 = 8.5 + 1 Reorder the terms: 1 + -2t + t2 = 8.5 + 1 Combine like terms: 8.5 + 1 = 9.5 1 + -2t + t2 = 9.5 Factor a perfect square on the left side: (t + -1)(t + -1) = 9.5 Calculate the square root of the right side: 3.082207001 Break this problem into two subproblems by setting (t + -1) equal to 3.082207001 and -3.082207001.Subproblem 1
t + -1 = 3.082207001 Simplifying t + -1 = 3.082207001 Reorder the terms: -1 + t = 3.082207001 Solving -1 + t = 3.082207001 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + t = 3.082207001 + 1 Combine like terms: -1 + 1 = 0 0 + t = 3.082207001 + 1 t = 3.082207001 + 1 Combine like terms: 3.082207001 + 1 = 4.082207001 t = 4.082207001 Simplifying t = 4.082207001Subproblem 2
t + -1 = -3.082207001 Simplifying t + -1 = -3.082207001 Reorder the terms: -1 + t = -3.082207001 Solving -1 + t = -3.082207001 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + t = -3.082207001 + 1 Combine like terms: -1 + 1 = 0 0 + t = -3.082207001 + 1 t = -3.082207001 + 1 Combine like terms: -3.082207001 + 1 = -2.082207001 t = -2.082207001 Simplifying t = -2.082207001Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.082207001, -2.082207001}
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