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Simplifying 5t2 + -6t + -4 = 0 Reorder the terms: -4 + -6t + 5t2 = 0 Solving -4 + -6t + 5t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.8 + -1.2t + t2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + -1.2t + 0.8 + t2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + -1.2t + t2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + -1.2t + t2 = 0 + 0.8 -1.2t + t2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 -1.2t + t2 = 0.8 The t term is -1.2t. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2t + 0.36 + t2 = 0.8 + 0.36 Reorder the terms: 0.36 + -1.2t + t2 = 0.8 + 0.36 Combine like terms: 0.8 + 0.36 = 1.16 0.36 + -1.2t + t2 = 1.16 Factor a perfect square on the left side: (t + -0.6)(t + -0.6) = 1.16 Calculate the square root of the right side: 1.077032961 Break this problem into two subproblems by setting (t + -0.6) equal to 1.077032961 and -1.077032961.Subproblem 1
t + -0.6 = 1.077032961 Simplifying t + -0.6 = 1.077032961 Reorder the terms: -0.6 + t = 1.077032961 Solving -0.6 + t = 1.077032961 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + t = 1.077032961 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + t = 1.077032961 + 0.6 t = 1.077032961 + 0.6 Combine like terms: 1.077032961 + 0.6 = 1.677032961 t = 1.677032961 Simplifying t = 1.677032961Subproblem 2
t + -0.6 = -1.077032961 Simplifying t + -0.6 = -1.077032961 Reorder the terms: -0.6 + t = -1.077032961 Solving -0.6 + t = -1.077032961 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + t = -1.077032961 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + t = -1.077032961 + 0.6 t = -1.077032961 + 0.6 Combine like terms: -1.077032961 + 0.6 = -0.477032961 t = -0.477032961 Simplifying t = -0.477032961Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.677032961, -0.477032961}
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