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Simplifying -7t2 + -3t + 7 = 0 Reorder the terms: 7 + -3t + -7t2 = 0 Solving 7 + -3t + -7t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -1 + 0.4285714286t + t2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 0.4285714286t + 1 + t2 = 0 + 1 Reorder the terms: -1 + 1 + 0.4285714286t + t2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 0.4285714286t + t2 = 0 + 1 0.4285714286t + t2 = 0 + 1 Combine like terms: 0 + 1 = 1 0.4285714286t + t2 = 1 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 = 1 + 0.04591836735 Reorder the terms: 0.04591836735 + 0.4285714286t + t2 = 1 + 0.04591836735 Combine like terms: 1 + 0.04591836735 = 1.04591836735 0.04591836735 + 0.4285714286t + t2 = 1.04591836735 Factor a perfect square on the left side: (t + 0.2142857143)(t + 0.2142857143) = 1.04591836735 Calculate the square root of the right side: 1.022701505 Break this problem into two subproblems by setting (t + 0.2142857143) equal to 1.022701505 and -1.022701505.Subproblem 1
t + 0.2142857143 = 1.022701505 Simplifying t + 0.2142857143 = 1.022701505 Reorder the terms: 0.2142857143 + t = 1.022701505 Solving 0.2142857143 + t = 1.022701505 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 = 1.022701505 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + t = 1.022701505 + -0.2142857143 t = 1.022701505 + -0.2142857143 Combine like terms: 1.022701505 + -0.2142857143 = 0.8084157907 t = 0.8084157907 Simplifying t = 0.8084157907Subproblem 2
t + 0.2142857143 = -1.022701505 Simplifying t + 0.2142857143 = -1.022701505 Reorder the terms: 0.2142857143 + t = -1.022701505 Solving 0.2142857143 + t = -1.022701505 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 = -1.022701505 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + t = -1.022701505 + -0.2142857143 t = -1.022701505 + -0.2142857143 Combine like terms: -1.022701505 + -0.2142857143 = -1.2369872193 t = -1.2369872193 Simplifying t = -1.2369872193Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.8084157907, -1.2369872193}
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