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Simplifying t2 + -5t = 7 Reorder the terms: -5t + t2 = 7 Solving -5t + t2 = 7 Solving for variable 't'. Reorder the terms: -7 + -5t + t2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + -5t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + -5t + 7 + t2 = 0 + 7 Reorder the terms: -7 + 7 + -5t + t2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -5t + t2 = 0 + 7 -5t + t2 = 0 + 7 Combine like terms: 0 + 7 = 7 -5t + t2 = 7 The t term is -5t. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5t + 6.25 + t2 = 7 + 6.25 Reorder the terms: 6.25 + -5t + t2 = 7 + 6.25 Combine like terms: 7 + 6.25 = 13.25 6.25 + -5t + t2 = 13.25 Factor a perfect square on the left side: (t + -2.5)(t + -2.5) = 13.25 Calculate the square root of the right side: 3.640054945 Break this problem into two subproblems by setting (t + -2.5) equal to 3.640054945 and -3.640054945.Subproblem 1
t + -2.5 = 3.640054945 Simplifying t + -2.5 = 3.640054945 Reorder the terms: -2.5 + t = 3.640054945 Solving -2.5 + t = 3.640054945 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = 3.640054945 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = 3.640054945 + 2.5 t = 3.640054945 + 2.5 Combine like terms: 3.640054945 + 2.5 = 6.140054945 t = 6.140054945 Simplifying t = 6.140054945Subproblem 2
t + -2.5 = -3.640054945 Simplifying t + -2.5 = -3.640054945 Reorder the terms: -2.5 + t = -3.640054945 Solving -2.5 + t = -3.640054945 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = -3.640054945 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = -3.640054945 + 2.5 t = -3.640054945 + 2.5 Combine like terms: -3.640054945 + 2.5 = -1.140054945 t = -1.140054945 Simplifying t = -1.140054945Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.140054945, -1.140054945}
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