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Simplifying 0 = -4.9t2 + 25t + 22 Reorder the terms: 0 = 22 + 25t + -4.9t2 Solving 0 = 22 + 25t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -22 = -22 -22 + -25t + 4.9t2 = 22 + 25t + -4.9t2 + -22 + -25t + 4.9t2 Reorder the terms: -22 + -25t + 4.9t2 = 22 + -22 + 25t + -25t + -4.9t2 + 4.9t2 Combine like terms: 22 + -22 = 0 -22 + -25t + 4.9t2 = 0 + 25t + -25t + -4.9t2 + 4.9t2 -22 + -25t + 4.9t2 = 25t + -25t + -4.9t2 + 4.9t2 Combine like terms: 25t + -25t = 0 -22 + -25t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -22 + -25t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -22 + -25t + 4.9t2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -4.489795918 + -5.102040816t + t2 = 0 Move the constant term to the right: Add '4.489795918' to each side of the equation. -4.489795918 + -5.102040816t + 4.489795918 + t2 = 0 + 4.489795918 Reorder the terms: -4.489795918 + 4.489795918 + -5.102040816t + t2 = 0 + 4.489795918 Combine like terms: -4.489795918 + 4.489795918 = 0.000000000 0.000000000 + -5.102040816t + t2 = 0 + 4.489795918 -5.102040816t + t2 = 0 + 4.489795918 Combine like terms: 0 + 4.489795918 = 4.489795918 -5.102040816t + t2 = 4.489795918 The t term is -5.102040816t. Take half its coefficient (-2.551020408). Square it (6.507705122) and add it to both sides. Add '6.507705122' to each side of the equation. -5.102040816t + 6.507705122 + t2 = 4.489795918 + 6.507705122 Reorder the terms: 6.507705122 + -5.102040816t + t2 = 4.489795918 + 6.507705122 Combine like terms: 4.489795918 + 6.507705122 = 10.99750104 6.507705122 + -5.102040816t + t2 = 10.99750104 Factor a perfect square on the left side: (t + -2.551020408)(t + -2.551020408) = 10.99750104 Calculate the square root of the right side: 3.316248037 Break this problem into two subproblems by setting (t + -2.551020408) equal to 3.316248037 and -3.316248037.Subproblem 1
t + -2.551020408 = 3.316248037 Simplifying t + -2.551020408 = 3.316248037 Reorder the terms: -2.551020408 + t = 3.316248037 Solving -2.551020408 + t = 3.316248037 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.551020408' to each side of the equation. -2.551020408 + 2.551020408 + t = 3.316248037 + 2.551020408 Combine like terms: -2.551020408 + 2.551020408 = 0.000000000 0.000000000 + t = 3.316248037 + 2.551020408 t = 3.316248037 + 2.551020408 Combine like terms: 3.316248037 + 2.551020408 = 5.867268445 t = 5.867268445 Simplifying t = 5.867268445Subproblem 2
t + -2.551020408 = -3.316248037 Simplifying t + -2.551020408 = -3.316248037 Reorder the terms: -2.551020408 + t = -3.316248037 Solving -2.551020408 + t = -3.316248037 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.551020408' to each side of the equation. -2.551020408 + 2.551020408 + t = -3.316248037 + 2.551020408 Combine like terms: -2.551020408 + 2.551020408 = 0.000000000 0.000000000 + t = -3.316248037 + 2.551020408 t = -3.316248037 + 2.551020408 Combine like terms: -3.316248037 + 2.551020408 = -0.765227629 t = -0.765227629 Simplifying t = -0.765227629Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.867268445, -0.765227629}
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