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Simplifying (5t2 + -2t) + -1(4t + 3) = 0 Reorder the terms: (-2t + 5t2) + -1(4t + 3) = 0 Remove parenthesis around (-2t + 5t2) -2t + 5t2 + -1(4t + 3) = 0 Reorder the terms: -2t + 5t2 + -1(3 + 4t) = 0 -2t + 5t2 + (3 * -1 + 4t * -1) = 0 -2t + 5t2 + (-3 + -4t) = 0 Reorder the terms: -3 + -2t + -4t + 5t2 = 0 Combine like terms: -2t + -4t = -6t -3 + -6t + 5t2 = 0 Solving -3 + -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'. -0.6 + -1.2t + t2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -1.2t + 0.6 + t2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + -1.2t + t2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -1.2t + t2 = 0 + 0.6 -1.2t + t2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 -1.2t + t2 = 0.6 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 = 0.6 + 0.36 Reorder the terms: 0.36 + -1.2t + t2 = 0.6 + 0.36 Combine like terms: 0.6 + 0.36 = 0.96 0.36 + -1.2t + t2 = 0.96 Factor a perfect square on the left side: (t + -0.6)(t + -0.6) = 0.96 Calculate the square root of the right side: 0.979795897 Break this problem into two subproblems by setting (t + -0.6) equal to 0.979795897 and -0.979795897.Subproblem 1
t + -0.6 = 0.979795897 Simplifying t + -0.6 = 0.979795897 Reorder the terms: -0.6 + t = 0.979795897 Solving -0.6 + t = 0.979795897 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 = 0.979795897 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + t = 0.979795897 + 0.6 t = 0.979795897 + 0.6 Combine like terms: 0.979795897 + 0.6 = 1.579795897 t = 1.579795897 Simplifying t = 1.579795897Subproblem 2
t + -0.6 = -0.979795897 Simplifying t + -0.6 = -0.979795897 Reorder the terms: -0.6 + t = -0.979795897 Solving -0.6 + t = -0.979795897 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 = -0.979795897 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + t = -0.979795897 + 0.6 t = -0.979795897 + 0.6 Combine like terms: -0.979795897 + 0.6 = -0.379795897 t = -0.379795897 Simplifying t = -0.379795897Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.579795897, -0.379795897}
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