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Simplifying -2.7t2 + 40t + 6.5 = 12 Reorder the terms: 6.5 + 40t + -2.7t2 = 12 Solving 6.5 + 40t + -2.7t2 = 12 Solving for variable 't'. Reorder the terms: 6.5 + -12 + 40t + -2.7t2 = 12 + -12 Combine like terms: 6.5 + -12 = -5.5 -5.5 + 40t + -2.7t2 = 12 + -12 Combine like terms: 12 + -12 = 0 -5.5 + 40t + -2.7t2 = 0 Begin completing the square. Divide all terms by -2.7 the coefficient of the squared term: Divide each side by '-2.7'. 2.037037037 + -14.81481481t + t2 = 0 Move the constant term to the right: Add '-2.037037037' to each side of the equation. 2.037037037 + -14.81481481t + -2.037037037 + t2 = 0 + -2.037037037 Reorder the terms: 2.037037037 + -2.037037037 + -14.81481481t + t2 = 0 + -2.037037037 Combine like terms: 2.037037037 + -2.037037037 = 0.000000000 0.000000000 + -14.81481481t + t2 = 0 + -2.037037037 -14.81481481t + t2 = 0 + -2.037037037 Combine like terms: 0 + -2.037037037 = -2.037037037 -14.81481481t + t2 = -2.037037037 The t term is -14.81481481t. Take half its coefficient (-7.407407405). Square it (54.86968446) and add it to both sides. Add '54.86968446' to each side of the equation. -14.81481481t + 54.86968446 + t2 = -2.037037037 + 54.86968446 Reorder the terms: 54.86968446 + -14.81481481t + t2 = -2.037037037 + 54.86968446 Combine like terms: -2.037037037 + 54.86968446 = 52.832647423 54.86968446 + -14.81481481t + t2 = 52.832647423 Factor a perfect square on the left side: (t + -7.407407405)(t + -7.407407405) = 52.832647423 Calculate the square root of the right side: 7.26860698 Break this problem into two subproblems by setting (t + -7.407407405) equal to 7.26860698 and -7.26860698.Subproblem 1
t + -7.407407405 = 7.26860698 Simplifying t + -7.407407405 = 7.26860698 Reorder the terms: -7.407407405 + t = 7.26860698 Solving -7.407407405 + t = 7.26860698 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7.407407405' to each side of the equation. -7.407407405 + 7.407407405 + t = 7.26860698 + 7.407407405 Combine like terms: -7.407407405 + 7.407407405 = 0.000000000 0.000000000 + t = 7.26860698 + 7.407407405 t = 7.26860698 + 7.407407405 Combine like terms: 7.26860698 + 7.407407405 = 14.676014385 t = 14.676014385 Simplifying t = 14.676014385Subproblem 2
t + -7.407407405 = -7.26860698 Simplifying t + -7.407407405 = -7.26860698 Reorder the terms: -7.407407405 + t = -7.26860698 Solving -7.407407405 + t = -7.26860698 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7.407407405' to each side of the equation. -7.407407405 + 7.407407405 + t = -7.26860698 + 7.407407405 Combine like terms: -7.407407405 + 7.407407405 = 0.000000000 0.000000000 + t = -7.26860698 + 7.407407405 t = -7.26860698 + 7.407407405 Combine like terms: -7.26860698 + 7.407407405 = 0.138800425 t = 0.138800425 Simplifying t = 0.138800425Solution
The solution to the problem is based on the solutions from the subproblems. t = {14.676014385, 0.138800425}
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