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Simplifying t2 + -10t + -80 = 0 Reorder the terms: -80 + -10t + t2 = 0 Solving -80 + -10t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '80' to each side of the equation. -80 + -10t + 80 + t2 = 0 + 80 Reorder the terms: -80 + 80 + -10t + t2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + -10t + t2 = 0 + 80 -10t + t2 = 0 + 80 Combine like terms: 0 + 80 = 80 -10t + t2 = 80 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 = 80 + 25 Reorder the terms: 25 + -10t + t2 = 80 + 25 Combine like terms: 80 + 25 = 105 25 + -10t + t2 = 105 Factor a perfect square on the left side: (t + -5)(t + -5) = 105 Calculate the square root of the right side: 10.246950766 Break this problem into two subproblems by setting (t + -5) equal to 10.246950766 and -10.246950766.Subproblem 1
t + -5 = 10.246950766 Simplifying t + -5 = 10.246950766 Reorder the terms: -5 + t = 10.246950766 Solving -5 + t = 10.246950766 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 = 10.246950766 + 5 Combine like terms: -5 + 5 = 0 0 + t = 10.246950766 + 5 t = 10.246950766 + 5 Combine like terms: 10.246950766 + 5 = 15.246950766 t = 15.246950766 Simplifying t = 15.246950766Subproblem 2
t + -5 = -10.246950766 Simplifying t + -5 = -10.246950766 Reorder the terms: -5 + t = -10.246950766 Solving -5 + t = -10.246950766 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 = -10.246950766 + 5 Combine like terms: -5 + 5 = 0 0 + t = -10.246950766 + 5 t = -10.246950766 + 5 Combine like terms: -10.246950766 + 5 = -5.246950766 t = -5.246950766 Simplifying t = -5.246950766Solution
The solution to the problem is based on the solutions from the subproblems. t = {15.246950766, -5.246950766}
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