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Simplifying t2 + -10t + 15 = 0 Reorder the terms: 15 + -10t + t2 = 0 Solving 15 + -10t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + -10t + -15 + t2 = 0 + -15 Reorder the terms: 15 + -15 + -10t + t2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -10t + t2 = 0 + -15 -10t + t2 = 0 + -15 Combine like terms: 0 + -15 = -15 -10t + t2 = -15 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 = -15 + 25 Reorder the terms: 25 + -10t + t2 = -15 + 25 Combine like terms: -15 + 25 = 10 25 + -10t + t2 = 10 Factor a perfect square on the left side: (t + -5)(t + -5) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (t + -5) equal to 3.16227766 and -3.16227766.Subproblem 1
t + -5 = 3.16227766 Simplifying t + -5 = 3.16227766 Reorder the terms: -5 + t = 3.16227766 Solving -5 + t = 3.16227766 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 = 3.16227766 + 5 Combine like terms: -5 + 5 = 0 0 + t = 3.16227766 + 5 t = 3.16227766 + 5 Combine like terms: 3.16227766 + 5 = 8.16227766 t = 8.16227766 Simplifying t = 8.16227766Subproblem 2
t + -5 = -3.16227766 Simplifying t + -5 = -3.16227766 Reorder the terms: -5 + t = -3.16227766 Solving -5 + t = -3.16227766 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 = -3.16227766 + 5 Combine like terms: -5 + 5 = 0 0 + t = -3.16227766 + 5 t = -3.16227766 + 5 Combine like terms: -3.16227766 + 5 = 1.83772234 t = 1.83772234 Simplifying t = 1.83772234Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.16227766, 1.83772234}
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