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Simplifying 7t2 + -15t + 7 = 4 Reorder the terms: 7 + -15t + 7t2 = 4 Solving 7 + -15t + 7t2 = 4 Solving for variable 't'. Reorder the terms: 7 + -4 + -15t + 7t2 = 4 + -4 Combine like terms: 7 + -4 = 3 3 + -15t + 7t2 = 4 + -4 Combine like terms: 4 + -4 = 0 3 + -15t + 7t2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.4285714286 + -2.142857143t + t2 = 0 Move the constant term to the right: Add '-0.4285714286' to each side of the equation. 0.4285714286 + -2.142857143t + -0.4285714286 + t2 = 0 + -0.4285714286 Reorder the terms: 0.4285714286 + -0.4285714286 + -2.142857143t + t2 = 0 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + -2.142857143t + t2 = 0 + -0.4285714286 -2.142857143t + t2 = 0 + -0.4285714286 Combine like terms: 0 + -0.4285714286 = -0.4285714286 -2.142857143t + t2 = -0.4285714286 The t term is -2.142857143t. Take half its coefficient (-1.071428572). Square it (1.147959185) and add it to both sides. Add '1.147959185' to each side of the equation. -2.142857143t + 1.147959185 + t2 = -0.4285714286 + 1.147959185 Reorder the terms: 1.147959185 + -2.142857143t + t2 = -0.4285714286 + 1.147959185 Combine like terms: -0.4285714286 + 1.147959185 = 0.7193877564 1.147959185 + -2.142857143t + t2 = 0.7193877564 Factor a perfect square on the left side: (t + -1.071428572)(t + -1.071428572) = 0.7193877564 Calculate the square root of the right side: 0.848167293 Break this problem into two subproblems by setting (t + -1.071428572) equal to 0.848167293 and -0.848167293.Subproblem 1
t + -1.071428572 = 0.848167293 Simplifying t + -1.071428572 = 0.848167293 Reorder the terms: -1.071428572 + t = 0.848167293 Solving -1.071428572 + t = 0.848167293 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.071428572' to each side of the equation. -1.071428572 + 1.071428572 + t = 0.848167293 + 1.071428572 Combine like terms: -1.071428572 + 1.071428572 = 0.000000000 0.000000000 + t = 0.848167293 + 1.071428572 t = 0.848167293 + 1.071428572 Combine like terms: 0.848167293 + 1.071428572 = 1.919595865 t = 1.919595865 Simplifying t = 1.919595865Subproblem 2
t + -1.071428572 = -0.848167293 Simplifying t + -1.071428572 = -0.848167293 Reorder the terms: -1.071428572 + t = -0.848167293 Solving -1.071428572 + t = -0.848167293 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.071428572' to each side of the equation. -1.071428572 + 1.071428572 + t = -0.848167293 + 1.071428572 Combine like terms: -1.071428572 + 1.071428572 = 0.000000000 0.000000000 + t = -0.848167293 + 1.071428572 t = -0.848167293 + 1.071428572 Combine like terms: -0.848167293 + 1.071428572 = 0.223261279 t = 0.223261279 Simplifying t = 0.223261279Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.919595865, 0.223261279}
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