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Simplifying 7.14 = 7t2 + 35t Reorder the terms: 7.14 = 35t + 7t2 Solving 7.14 = 35t + 7t2 Solving for variable 't'. Reorder the terms: 7.14 + -35t + -7t2 = 35t + -35t + 7t2 + -7t2 Combine like terms: 35t + -35t = 0 7.14 + -35t + -7t2 = 0 + 7t2 + -7t2 7.14 + -35t + -7t2 = 7t2 + -7t2 Combine like terms: 7t2 + -7t2 = 0 7.14 + -35t + -7t2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -1.02 + 5t + t2 = 0 Move the constant term to the right: Add '1.02' to each side of the equation. -1.02 + 5t + 1.02 + t2 = 0 + 1.02 Reorder the terms: -1.02 + 1.02 + 5t + t2 = 0 + 1.02 Combine like terms: -1.02 + 1.02 = 0.00 0.00 + 5t + t2 = 0 + 1.02 5t + t2 = 0 + 1.02 Combine like terms: 0 + 1.02 = 1.02 5t + t2 = 1.02 The t term is 5t. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5t + 6.25 + t2 = 1.02 + 6.25 Reorder the terms: 6.25 + 5t + t2 = 1.02 + 6.25 Combine like terms: 1.02 + 6.25 = 7.27 6.25 + 5t + t2 = 7.27 Factor a perfect square on the left side: (t + 2.5)(t + 2.5) = 7.27 Calculate the square root of the right side: 2.696293753 Break this problem into two subproblems by setting (t + 2.5) equal to 2.696293753 and -2.696293753.Subproblem 1
t + 2.5 = 2.696293753 Simplifying t + 2.5 = 2.696293753 Reorder the terms: 2.5 + t = 2.696293753 Solving 2.5 + t = 2.696293753 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + t = 2.696293753 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + t = 2.696293753 + -2.5 t = 2.696293753 + -2.5 Combine like terms: 2.696293753 + -2.5 = 0.196293753 t = 0.196293753 Simplifying t = 0.196293753Subproblem 2
t + 2.5 = -2.696293753 Simplifying t + 2.5 = -2.696293753 Reorder the terms: 2.5 + t = -2.696293753 Solving 2.5 + t = -2.696293753 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + t = -2.696293753 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + t = -2.696293753 + -2.5 t = -2.696293753 + -2.5 Combine like terms: -2.696293753 + -2.5 = -5.196293753 t = -5.196293753 Simplifying t = -5.196293753Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.196293753, -5.196293753}
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