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Simplifying 0 = 7 + 36t + -16t2 Solving 0 = 7 + 36t + -16t2 Solving for variable 't'. Combine like terms: 0 + -7 = -7 -7 + -36t + 16t2 = 7 + 36t + -16t2 + -7 + -36t + 16t2 Reorder the terms: -7 + -36t + 16t2 = 7 + -7 + 36t + -36t + -16t2 + 16t2 Combine like terms: 7 + -7 = 0 -7 + -36t + 16t2 = 0 + 36t + -36t + -16t2 + 16t2 -7 + -36t + 16t2 = 36t + -36t + -16t2 + 16t2 Combine like terms: 36t + -36t = 0 -7 + -36t + 16t2 = 0 + -16t2 + 16t2 -7 + -36t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -7 + -36t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.4375 + -2.25t + t2 = 0 Move the constant term to the right: Add '0.4375' to each side of the equation. -0.4375 + -2.25t + 0.4375 + t2 = 0 + 0.4375 Reorder the terms: -0.4375 + 0.4375 + -2.25t + t2 = 0 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + -2.25t + t2 = 0 + 0.4375 -2.25t + t2 = 0 + 0.4375 Combine like terms: 0 + 0.4375 = 0.4375 -2.25t + t2 = 0.4375 The t term is -2.25t. Take half its coefficient (-1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. -2.25t + 1.265625 + t2 = 0.4375 + 1.265625 Reorder the terms: 1.265625 + -2.25t + t2 = 0.4375 + 1.265625 Combine like terms: 0.4375 + 1.265625 = 1.703125 1.265625 + -2.25t + t2 = 1.703125 Factor a perfect square on the left side: (t + -1.125)(t + -1.125) = 1.703125 Calculate the square root of the right side: 1.305038314 Break this problem into two subproblems by setting (t + -1.125) equal to 1.305038314 and -1.305038314.Subproblem 1
t + -1.125 = 1.305038314 Simplifying t + -1.125 = 1.305038314 Reorder the terms: -1.125 + t = 1.305038314 Solving -1.125 + t = 1.305038314 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + t = 1.305038314 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + t = 1.305038314 + 1.125 t = 1.305038314 + 1.125 Combine like terms: 1.305038314 + 1.125 = 2.430038314 t = 2.430038314 Simplifying t = 2.430038314Subproblem 2
t + -1.125 = -1.305038314 Simplifying t + -1.125 = -1.305038314 Reorder the terms: -1.125 + t = -1.305038314 Solving -1.125 + t = -1.305038314 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + t = -1.305038314 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + t = -1.305038314 + 1.125 t = -1.305038314 + 1.125 Combine like terms: -1.305038314 + 1.125 = -0.180038314 t = -0.180038314 Simplifying t = -0.180038314Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.430038314, -0.180038314}
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