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Simplifying 4t2 + -3t = 5 + -3t2 Reorder the terms: -3t + 4t2 = 5 + -3t2 Solving -3t + 4t2 = 5 + -3t2 Solving for variable 't'. Reorder the terms: -5 + -3t + 4t2 + 3t2 = 5 + -3t2 + -5 + 3t2 Combine like terms: 4t2 + 3t2 = 7t2 -5 + -3t + 7t2 = 5 + -3t2 + -5 + 3t2 Reorder the terms: -5 + -3t + 7t2 = 5 + -5 + -3t2 + 3t2 Combine like terms: 5 + -5 = 0 -5 + -3t + 7t2 = 0 + -3t2 + 3t2 -5 + -3t + 7t2 = -3t2 + 3t2 Combine like terms: -3t2 + 3t2 = 0 -5 + -3t + 7t2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.7142857143 + -0.4285714286t + t2 = 0 Move the constant term to the right: Add '0.7142857143' to each side of the equation. -0.7142857143 + -0.4285714286t + 0.7142857143 + t2 = 0 + 0.7142857143 Reorder the terms: -0.7142857143 + 0.7142857143 + -0.4285714286t + t2 = 0 + 0.7142857143 Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000 0.0000000000 + -0.4285714286t + t2 = 0 + 0.7142857143 -0.4285714286t + t2 = 0 + 0.7142857143 Combine like terms: 0 + 0.7142857143 = 0.7142857143 -0.4285714286t + t2 = 0.7142857143 The t term is -0.4285714286t. Take half its coefficient (-0.2142857143). Square it (0.04591836735) and add it to both sides. Add '0.04591836735' to each side of the equation. -0.4285714286t + 0.04591836735 + t2 = 0.7142857143 + 0.04591836735 Reorder the terms: 0.04591836735 + -0.4285714286t + t2 = 0.7142857143 + 0.04591836735 Combine like terms: 0.7142857143 + 0.04591836735 = 0.76020408165 0.04591836735 + -0.4285714286t + t2 = 0.76020408165 Factor a perfect square on the left side: (t + -0.2142857143)(t + -0.2142857143) = 0.76020408165 Calculate the square root of the right side: 0.87189683 Break this problem into two subproblems by setting (t + -0.2142857143) equal to 0.87189683 and -0.87189683.Subproblem 1
t + -0.2142857143 = 0.87189683 Simplifying t + -0.2142857143 = 0.87189683 Reorder the terms: -0.2142857143 + t = 0.87189683 Solving -0.2142857143 + t = 0.87189683 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.2142857143' to each side of the equation. -0.2142857143 + 0.2142857143 + t = 0.87189683 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + t = 0.87189683 + 0.2142857143 t = 0.87189683 + 0.2142857143 Combine like terms: 0.87189683 + 0.2142857143 = 1.0861825443 t = 1.0861825443 Simplifying t = 1.0861825443Subproblem 2
t + -0.2142857143 = -0.87189683 Simplifying t + -0.2142857143 = -0.87189683 Reorder the terms: -0.2142857143 + t = -0.87189683 Solving -0.2142857143 + t = -0.87189683 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.2142857143' to each side of the equation. -0.2142857143 + 0.2142857143 + t = -0.87189683 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + t = -0.87189683 + 0.2142857143 t = -0.87189683 + 0.2142857143 Combine like terms: -0.87189683 + 0.2142857143 = -0.6576111157 t = -0.6576111157 Simplifying t = -0.6576111157Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.0861825443, -0.6576111157}
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