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Simplifying 10 = t2 + -8t Reorder the terms: 10 = -8t + t2 Solving 10 = -8t + t2 Solving for variable 't'. Reorder the terms: 10 + 8t + -1t2 = -8t + 8t + t2 + -1t2 Combine like terms: -8t + 8t = 0 10 + 8t + -1t2 = 0 + t2 + -1t2 10 + 8t + -1t2 = t2 + -1t2 Combine like terms: t2 + -1t2 = 0 10 + 8t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -10 + -8t + t2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -8t + 10 + t2 = 0 + 10 Reorder the terms: -10 + 10 + -8t + t2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -8t + t2 = 0 + 10 -8t + t2 = 0 + 10 Combine like terms: 0 + 10 = 10 -8t + t2 = 10 The t term is -8t. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8t + 16 + t2 = 10 + 16 Reorder the terms: 16 + -8t + t2 = 10 + 16 Combine like terms: 10 + 16 = 26 16 + -8t + t2 = 26 Factor a perfect square on the left side: (t + -4)(t + -4) = 26 Calculate the square root of the right side: 5.099019514 Break this problem into two subproblems by setting (t + -4) equal to 5.099019514 and -5.099019514.Subproblem 1
t + -4 = 5.099019514 Simplifying t + -4 = 5.099019514 Reorder the terms: -4 + t = 5.099019514 Solving -4 + t = 5.099019514 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = 5.099019514 + 4 Combine like terms: -4 + 4 = 0 0 + t = 5.099019514 + 4 t = 5.099019514 + 4 Combine like terms: 5.099019514 + 4 = 9.099019514 t = 9.099019514 Simplifying t = 9.099019514Subproblem 2
t + -4 = -5.099019514 Simplifying t + -4 = -5.099019514 Reorder the terms: -4 + t = -5.099019514 Solving -4 + t = -5.099019514 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = -5.099019514 + 4 Combine like terms: -4 + 4 = 0 0 + t = -5.099019514 + 4 t = -5.099019514 + 4 Combine like terms: -5.099019514 + 4 = -1.099019514 t = -1.099019514 Simplifying t = -1.099019514Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.099019514, -1.099019514}
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