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Simplifying 1.4t2 = 3.0t + 7 Reorder the terms: 1.4t2 = 7 + 3.0t Solving 1.4t2 = 7 + 3.0t Solving for variable 't'. Reorder the terms: -7 + -3.0t + 1.4t2 = 7 + 3.0t + -7 + -3.0t Reorder the terms: -7 + -3.0t + 1.4t2 = 7 + -7 + 3.0t + -3.0t Combine like terms: 7 + -7 = 0 -7 + -3.0t + 1.4t2 = 0 + 3.0t + -3.0t -7 + -3.0t + 1.4t2 = 3.0t + -3.0t Combine like terms: 3.0t + -3.0t = 0.0 -7 + -3.0t + 1.4t2 = 0.0 Begin completing the square. Divide all terms by 1.4 the coefficient of the squared term: Divide each side by '1.4'. -5 + -2.142857143t + t2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -2.142857143t + 5 + t2 = 0 + 5 Reorder the terms: -5 + 5 + -2.142857143t + t2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2.142857143t + t2 = 0 + 5 -2.142857143t + t2 = 0 + 5 Combine like terms: 0 + 5 = 5 -2.142857143t + t2 = 5 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 = 5 + 1.147959185 Reorder the terms: 1.147959185 + -2.142857143t + t2 = 5 + 1.147959185 Combine like terms: 5 + 1.147959185 = 6.147959185 1.147959185 + -2.142857143t + t2 = 6.147959185 Factor a perfect square on the left side: (t + -1.071428572)(t + -1.071428572) = 6.147959185 Calculate the square root of the right side: 2.479507851 Break this problem into two subproblems by setting (t + -1.071428572) equal to 2.479507851 and -2.479507851.Subproblem 1
t + -1.071428572 = 2.479507851 Simplifying t + -1.071428572 = 2.479507851 Reorder the terms: -1.071428572 + t = 2.479507851 Solving -1.071428572 + t = 2.479507851 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 = 2.479507851 + 1.071428572 Combine like terms: -1.071428572 + 1.071428572 = 0.000000000 0.000000000 + t = 2.479507851 + 1.071428572 t = 2.479507851 + 1.071428572 Combine like terms: 2.479507851 + 1.071428572 = 3.550936423 t = 3.550936423 Simplifying t = 3.550936423Subproblem 2
t + -1.071428572 = -2.479507851 Simplifying t + -1.071428572 = -2.479507851 Reorder the terms: -1.071428572 + t = -2.479507851 Solving -1.071428572 + t = -2.479507851 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 = -2.479507851 + 1.071428572 Combine like terms: -1.071428572 + 1.071428572 = 0.000000000 0.000000000 + t = -2.479507851 + 1.071428572 t = -2.479507851 + 1.071428572 Combine like terms: -2.479507851 + 1.071428572 = -1.408079279 t = -1.408079279 Simplifying t = -1.408079279Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.550936423, -1.408079279}
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