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Simplifying 0 = -16t2 + 144t + 7 Reorder the terms: 0 = 7 + 144t + -16t2 Solving 0 = 7 + 144t + -16t2 Solving for variable 't'. Combine like terms: 0 + -7 = -7 -7 + -144t + 16t2 = 7 + 144t + -16t2 + -7 + -144t + 16t2 Reorder the terms: -7 + -144t + 16t2 = 7 + -7 + 144t + -144t + -16t2 + 16t2 Combine like terms: 7 + -7 = 0 -7 + -144t + 16t2 = 0 + 144t + -144t + -16t2 + 16t2 -7 + -144t + 16t2 = 144t + -144t + -16t2 + 16t2 Combine like terms: 144t + -144t = 0 -7 + -144t + 16t2 = 0 + -16t2 + 16t2 -7 + -144t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -7 + -144t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.4375 + -9t + t2 = 0 Move the constant term to the right: Add '0.4375' to each side of the equation. -0.4375 + -9t + 0.4375 + t2 = 0 + 0.4375 Reorder the terms: -0.4375 + 0.4375 + -9t + t2 = 0 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + -9t + t2 = 0 + 0.4375 -9t + t2 = 0 + 0.4375 Combine like terms: 0 + 0.4375 = 0.4375 -9t + t2 = 0.4375 The t term is -9t. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9t + 20.25 + t2 = 0.4375 + 20.25 Reorder the terms: 20.25 + -9t + t2 = 0.4375 + 20.25 Combine like terms: 0.4375 + 20.25 = 20.6875 20.25 + -9t + t2 = 20.6875 Factor a perfect square on the left side: (t + -4.5)(t + -4.5) = 20.6875 Calculate the square root of the right side: 4.54835135 Break this problem into two subproblems by setting (t + -4.5) equal to 4.54835135 and -4.54835135.Subproblem 1
t + -4.5 = 4.54835135 Simplifying t + -4.5 = 4.54835135 Reorder the terms: -4.5 + t = 4.54835135 Solving -4.5 + t = 4.54835135 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + t = 4.54835135 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + t = 4.54835135 + 4.5 t = 4.54835135 + 4.5 Combine like terms: 4.54835135 + 4.5 = 9.04835135 t = 9.04835135 Simplifying t = 9.04835135Subproblem 2
t + -4.5 = -4.54835135 Simplifying t + -4.5 = -4.54835135 Reorder the terms: -4.5 + t = -4.54835135 Solving -4.5 + t = -4.54835135 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + t = -4.54835135 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + t = -4.54835135 + 4.5 t = -4.54835135 + 4.5 Combine like terms: -4.54835135 + 4.5 = -0.04835135 t = -0.04835135 Simplifying t = -0.04835135Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.04835135, -0.04835135}
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