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Simplifying 15 + 90t + -16t2 = 100 Solving 15 + 90t + -16t2 = 100 Solving for variable 't'. Reorder the terms: 15 + -100 + 90t + -16t2 = 100 + -100 Combine like terms: 15 + -100 = -85 -85 + 90t + -16t2 = 100 + -100 Combine like terms: 100 + -100 = 0 -85 + 90t + -16t2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 5.3125 + -5.625t + t2 = 0 Move the constant term to the right: Add '-5.3125' to each side of the equation. 5.3125 + -5.625t + -5.3125 + t2 = 0 + -5.3125 Reorder the terms: 5.3125 + -5.3125 + -5.625t + t2 = 0 + -5.3125 Combine like terms: 5.3125 + -5.3125 = 0.0000 0.0000 + -5.625t + t2 = 0 + -5.3125 -5.625t + t2 = 0 + -5.3125 Combine like terms: 0 + -5.3125 = -5.3125 -5.625t + t2 = -5.3125 The t term is -5.625t. Take half its coefficient (-2.8125). Square it (7.91015625) and add it to both sides. Add '7.91015625' to each side of the equation. -5.625t + 7.91015625 + t2 = -5.3125 + 7.91015625 Reorder the terms: 7.91015625 + -5.625t + t2 = -5.3125 + 7.91015625 Combine like terms: -5.3125 + 7.91015625 = 2.59765625 7.91015625 + -5.625t + t2 = 2.59765625 Factor a perfect square on the left side: (t + -2.8125)(t + -2.8125) = 2.59765625 Calculate the square root of the right side: 1.61172462 Break this problem into two subproblems by setting (t + -2.8125) equal to 1.61172462 and -1.61172462.Subproblem 1
t + -2.8125 = 1.61172462 Simplifying t + -2.8125 = 1.61172462 Reorder the terms: -2.8125 + t = 1.61172462 Solving -2.8125 + t = 1.61172462 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.8125' to each side of the equation. -2.8125 + 2.8125 + t = 1.61172462 + 2.8125 Combine like terms: -2.8125 + 2.8125 = 0.0000 0.0000 + t = 1.61172462 + 2.8125 t = 1.61172462 + 2.8125 Combine like terms: 1.61172462 + 2.8125 = 4.42422462 t = 4.42422462 Simplifying t = 4.42422462Subproblem 2
t + -2.8125 = -1.61172462 Simplifying t + -2.8125 = -1.61172462 Reorder the terms: -2.8125 + t = -1.61172462 Solving -2.8125 + t = -1.61172462 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.8125' to each side of the equation. -2.8125 + 2.8125 + t = -1.61172462 + 2.8125 Combine like terms: -2.8125 + 2.8125 = 0.0000 0.0000 + t = -1.61172462 + 2.8125 t = -1.61172462 + 2.8125 Combine like terms: -1.61172462 + 2.8125 = 1.20077538 t = 1.20077538 Simplifying t = 1.20077538Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.42422462, 1.20077538}
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