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Simplifying t2 + -10t + 6 = -7 Reorder the terms: 6 + -10t + t2 = -7 Solving 6 + -10t + t2 = -7 Solving for variable 't'. Reorder the terms: 6 + 7 + -10t + t2 = -7 + 7 Combine like terms: 6 + 7 = 13 13 + -10t + t2 = -7 + 7 Combine like terms: -7 + 7 = 0 13 + -10t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-13' to each side of the equation. 13 + -10t + -13 + t2 = 0 + -13 Reorder the terms: 13 + -13 + -10t + t2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -10t + t2 = 0 + -13 -10t + t2 = 0 + -13 Combine like terms: 0 + -13 = -13 -10t + t2 = -13 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 = -13 + 25 Reorder the terms: 25 + -10t + t2 = -13 + 25 Combine like terms: -13 + 25 = 12 25 + -10t + t2 = 12 Factor a perfect square on the left side: (t + -5)(t + -5) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (t + -5) equal to 3.464101615 and -3.464101615.Subproblem 1
t + -5 = 3.464101615 Simplifying t + -5 = 3.464101615 Reorder the terms: -5 + t = 3.464101615 Solving -5 + t = 3.464101615 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 = 3.464101615 + 5 Combine like terms: -5 + 5 = 0 0 + t = 3.464101615 + 5 t = 3.464101615 + 5 Combine like terms: 3.464101615 + 5 = 8.464101615 t = 8.464101615 Simplifying t = 8.464101615Subproblem 2
t + -5 = -3.464101615 Simplifying t + -5 = -3.464101615 Reorder the terms: -5 + t = -3.464101615 Solving -5 + t = -3.464101615 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 = -3.464101615 + 5 Combine like terms: -5 + 5 = 0 0 + t = -3.464101615 + 5 t = -3.464101615 + 5 Combine like terms: -3.464101615 + 5 = 1.535898385 t = 1.535898385 Simplifying t = 1.535898385Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.464101615, 1.535898385}
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