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Simplifying 64 + -16t2 = t Solving 64 + -16t2 = t Solving for variable 't'. Reorder the terms: 64 + -1t + -16t2 = t + -1t Combine like terms: t + -1t = 0 64 + -1t + -16t2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -4 + 0.0625t + t2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 0.0625t + 4 + t2 = 0 + 4 Reorder the terms: -4 + 4 + 0.0625t + t2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 0.0625t + t2 = 0 + 4 0.0625t + t2 = 0 + 4 Combine like terms: 0 + 4 = 4 0.0625t + t2 = 4 The t term is 0.0625t. Take half its coefficient (0.03125). Square it (0.0009765625) and add it to both sides. Add '0.0009765625' to each side of the equation. 0.0625t + 0.0009765625 + t2 = 4 + 0.0009765625 Reorder the terms: 0.0009765625 + 0.0625t + t2 = 4 + 0.0009765625 Combine like terms: 4 + 0.0009765625 = 4.0009765625 0.0009765625 + 0.0625t + t2 = 4.0009765625 Factor a perfect square on the left side: (t + 0.03125)(t + 0.03125) = 4.0009765625 Calculate the square root of the right side: 2.000244126 Break this problem into two subproblems by setting (t + 0.03125) equal to 2.000244126 and -2.000244126.Subproblem 1
t + 0.03125 = 2.000244126 Simplifying t + 0.03125 = 2.000244126 Reorder the terms: 0.03125 + t = 2.000244126 Solving 0.03125 + t = 2.000244126 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.03125' to each side of the equation. 0.03125 + -0.03125 + t = 2.000244126 + -0.03125 Combine like terms: 0.03125 + -0.03125 = 0.00000 0.00000 + t = 2.000244126 + -0.03125 t = 2.000244126 + -0.03125 Combine like terms: 2.000244126 + -0.03125 = 1.968994126 t = 1.968994126 Simplifying t = 1.968994126Subproblem 2
t + 0.03125 = -2.000244126 Simplifying t + 0.03125 = -2.000244126 Reorder the terms: 0.03125 + t = -2.000244126 Solving 0.03125 + t = -2.000244126 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.03125' to each side of the equation. 0.03125 + -0.03125 + t = -2.000244126 + -0.03125 Combine like terms: 0.03125 + -0.03125 = 0.00000 0.00000 + t = -2.000244126 + -0.03125 t = -2.000244126 + -0.03125 Combine like terms: -2.000244126 + -0.03125 = -2.031494126 t = -2.031494126 Simplifying t = -2.031494126Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.968994126, -2.031494126}
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