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Simplifying 5t2 + -6 = 8t Reorder the terms: -6 + 5t2 = 8t Solving -6 + 5t2 = 8t Solving for variable 't'. Reorder the terms: -6 + -8t + 5t2 = 8t + -8t Combine like terms: 8t + -8t = 0 -6 + -8t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.2 + -1.6t + t2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + -1.6t + 1.2 + t2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + -1.6t + t2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + -1.6t + t2 = 0 + 1.2 -1.6t + t2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 -1.6t + t2 = 1.2 The t term is -1.6t. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6t + 0.64 + t2 = 1.2 + 0.64 Reorder the terms: 0.64 + -1.6t + t2 = 1.2 + 0.64 Combine like terms: 1.2 + 0.64 = 1.84 0.64 + -1.6t + t2 = 1.84 Factor a perfect square on the left side: (t + -0.8)(t + -0.8) = 1.84 Calculate the square root of the right side: 1.356465997 Break this problem into two subproblems by setting (t + -0.8) equal to 1.356465997 and -1.356465997.Subproblem 1
t + -0.8 = 1.356465997 Simplifying t + -0.8 = 1.356465997 Reorder the terms: -0.8 + t = 1.356465997 Solving -0.8 + t = 1.356465997 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + t = 1.356465997 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + t = 1.356465997 + 0.8 t = 1.356465997 + 0.8 Combine like terms: 1.356465997 + 0.8 = 2.156465997 t = 2.156465997 Simplifying t = 2.156465997Subproblem 2
t + -0.8 = -1.356465997 Simplifying t + -0.8 = -1.356465997 Reorder the terms: -0.8 + t = -1.356465997 Solving -0.8 + t = -1.356465997 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + t = -1.356465997 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + t = -1.356465997 + 0.8 t = -1.356465997 + 0.8 Combine like terms: -1.356465997 + 0.8 = -0.556465997 t = -0.556465997 Simplifying t = -0.556465997Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.156465997, -0.556465997}
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