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Simplifying 0 = -4.8t2 + 6t + 8 Reorder the terms: 0 = 8 + 6t + -4.8t2 Solving 0 = 8 + 6t + -4.8t2 Solving for variable 't'. Combine like terms: 0 + -8 = -8 -8 + -6t + 4.8t2 = 8 + 6t + -4.8t2 + -8 + -6t + 4.8t2 Reorder the terms: -8 + -6t + 4.8t2 = 8 + -8 + 6t + -6t + -4.8t2 + 4.8t2 Combine like terms: 8 + -8 = 0 -8 + -6t + 4.8t2 = 0 + 6t + -6t + -4.8t2 + 4.8t2 -8 + -6t + 4.8t2 = 6t + -6t + -4.8t2 + 4.8t2 Combine like terms: 6t + -6t = 0 -8 + -6t + 4.8t2 = 0 + -4.8t2 + 4.8t2 -8 + -6t + 4.8t2 = -4.8t2 + 4.8t2 Combine like terms: -4.8t2 + 4.8t2 = 0.0 -8 + -6t + 4.8t2 = 0.0 Begin completing the square. Divide all terms by 4.8 the coefficient of the squared term: Divide each side by '4.8'. -1.666666667 + -1.25t + t2 = 0 Move the constant term to the right: Add '1.666666667' to each side of the equation. -1.666666667 + -1.25t + 1.666666667 + t2 = 0 + 1.666666667 Reorder the terms: -1.666666667 + 1.666666667 + -1.25t + t2 = 0 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + -1.25t + t2 = 0 + 1.666666667 -1.25t + t2 = 0 + 1.666666667 Combine like terms: 0 + 1.666666667 = 1.666666667 -1.25t + t2 = 1.666666667 The t term is -1.25t. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25t + 0.390625 + t2 = 1.666666667 + 0.390625 Reorder the terms: 0.390625 + -1.25t + t2 = 1.666666667 + 0.390625 Combine like terms: 1.666666667 + 0.390625 = 2.057291667 0.390625 + -1.25t + t2 = 2.057291667 Factor a perfect square on the left side: (t + -0.625)(t + -0.625) = 2.057291667 Calculate the square root of the right side: 1.434326207 Break this problem into two subproblems by setting (t + -0.625) equal to 1.434326207 and -1.434326207.Subproblem 1
t + -0.625 = 1.434326207 Simplifying t + -0.625 = 1.434326207 Reorder the terms: -0.625 + t = 1.434326207 Solving -0.625 + t = 1.434326207 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + t = 1.434326207 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + t = 1.434326207 + 0.625 t = 1.434326207 + 0.625 Combine like terms: 1.434326207 + 0.625 = 2.059326207 t = 2.059326207 Simplifying t = 2.059326207Subproblem 2
t + -0.625 = -1.434326207 Simplifying t + -0.625 = -1.434326207 Reorder the terms: -0.625 + t = -1.434326207 Solving -0.625 + t = -1.434326207 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + t = -1.434326207 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + t = -1.434326207 + 0.625 t = -1.434326207 + 0.625 Combine like terms: -1.434326207 + 0.625 = -0.809326207 t = -0.809326207 Simplifying t = -0.809326207Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.059326207, -0.809326207}
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