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Simplifying -16t2 + 160t + 5.5 = 0 Reorder the terms: 5.5 + 160t + -16t2 = 0 Solving 5.5 + 160t + -16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.34375 + -10t + t2 = 0 Move the constant term to the right: Add '0.34375' to each side of the equation. -0.34375 + -10t + 0.34375 + t2 = 0 + 0.34375 Reorder the terms: -0.34375 + 0.34375 + -10t + t2 = 0 + 0.34375 Combine like terms: -0.34375 + 0.34375 = 0.00000 0.00000 + -10t + t2 = 0 + 0.34375 -10t + t2 = 0 + 0.34375 Combine like terms: 0 + 0.34375 = 0.34375 -10t + t2 = 0.34375 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 = 0.34375 + 25 Reorder the terms: 25 + -10t + t2 = 0.34375 + 25 Combine like terms: 0.34375 + 25 = 25.34375 25 + -10t + t2 = 25.34375 Factor a perfect square on the left side: (t + -5)(t + -5) = 25.34375 Calculate the square root of the right side: 5.034257641 Break this problem into two subproblems by setting (t + -5) equal to 5.034257641 and -5.034257641.Subproblem 1
t + -5 = 5.034257641 Simplifying t + -5 = 5.034257641 Reorder the terms: -5 + t = 5.034257641 Solving -5 + t = 5.034257641 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 = 5.034257641 + 5 Combine like terms: -5 + 5 = 0 0 + t = 5.034257641 + 5 t = 5.034257641 + 5 Combine like terms: 5.034257641 + 5 = 10.034257641 t = 10.034257641 Simplifying t = 10.034257641Subproblem 2
t + -5 = -5.034257641 Simplifying t + -5 = -5.034257641 Reorder the terms: -5 + t = -5.034257641 Solving -5 + t = -5.034257641 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 = -5.034257641 + 5 Combine like terms: -5 + 5 = 0 0 + t = -5.034257641 + 5 t = -5.034257641 + 5 Combine like terms: -5.034257641 + 5 = -0.034257641 t = -0.034257641 Simplifying t = -0.034257641Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.034257641, -0.034257641}
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