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Simplifying t2 + -1t = 66 Reorder the terms: -1t + t2 = 66 Solving -1t + t2 = 66 Solving for variable 't'. Reorder the terms: -66 + -1t + t2 = 66 + -66 Combine like terms: 66 + -66 = 0 -66 + -1t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '66' to each side of the equation. -66 + -1t + 66 + t2 = 0 + 66 Reorder the terms: -66 + 66 + -1t + t2 = 0 + 66 Combine like terms: -66 + 66 = 0 0 + -1t + t2 = 0 + 66 -1t + t2 = 0 + 66 Combine like terms: 0 + 66 = 66 -1t + t2 = 66 The t term is -1t. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1t + 0.25 + t2 = 66 + 0.25 Reorder the terms: 0.25 + -1t + t2 = 66 + 0.25 Combine like terms: 66 + 0.25 = 66.25 0.25 + -1t + t2 = 66.25 Factor a perfect square on the left side: (t + -0.5)(t + -0.5) = 66.25 Calculate the square root of the right side: 8.139410298 Break this problem into two subproblems by setting (t + -0.5) equal to 8.139410298 and -8.139410298.Subproblem 1
t + -0.5 = 8.139410298 Simplifying t + -0.5 = 8.139410298 Reorder the terms: -0.5 + t = 8.139410298 Solving -0.5 + t = 8.139410298 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + t = 8.139410298 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = 8.139410298 + 0.5 t = 8.139410298 + 0.5 Combine like terms: 8.139410298 + 0.5 = 8.639410298 t = 8.639410298 Simplifying t = 8.639410298Subproblem 2
t + -0.5 = -8.139410298 Simplifying t + -0.5 = -8.139410298 Reorder the terms: -0.5 + t = -8.139410298 Solving -0.5 + t = -8.139410298 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + t = -8.139410298 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = -8.139410298 + 0.5 t = -8.139410298 + 0.5 Combine like terms: -8.139410298 + 0.5 = -7.639410298 t = -7.639410298 Simplifying t = -7.639410298Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.639410298, -7.639410298}
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