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Simplifying t2 + -10t + 8 = 0 Reorder the terms: 8 + -10t + t2 = 0 Solving 8 + -10t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + -10t + -8 + t2 = 0 + -8 Reorder the terms: 8 + -8 + -10t + t2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -10t + t2 = 0 + -8 -10t + t2 = 0 + -8 Combine like terms: 0 + -8 = -8 -10t + t2 = -8 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 = -8 + 25 Reorder the terms: 25 + -10t + t2 = -8 + 25 Combine like terms: -8 + 25 = 17 25 + -10t + t2 = 17 Factor a perfect square on the left side: (t + -5)(t + -5) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (t + -5) equal to 4.123105626 and -4.123105626.Subproblem 1
t + -5 = 4.123105626 Simplifying t + -5 = 4.123105626 Reorder the terms: -5 + t = 4.123105626 Solving -5 + t = 4.123105626 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 = 4.123105626 + 5 Combine like terms: -5 + 5 = 0 0 + t = 4.123105626 + 5 t = 4.123105626 + 5 Combine like terms: 4.123105626 + 5 = 9.123105626 t = 9.123105626 Simplifying t = 9.123105626Subproblem 2
t + -5 = -4.123105626 Simplifying t + -5 = -4.123105626 Reorder the terms: -5 + t = -4.123105626 Solving -5 + t = -4.123105626 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 = -4.123105626 + 5 Combine like terms: -5 + 5 = 0 0 + t = -4.123105626 + 5 t = -4.123105626 + 5 Combine like terms: -4.123105626 + 5 = 0.876894374 t = 0.876894374 Simplifying t = 0.876894374Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.123105626, 0.876894374}
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