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Simplifying 4.9t2 + 12.2t + -31 = 0 Reorder the terms: -31 + 12.2t + 4.9t2 = 0 Solving -31 + 12.2t + 4.9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -6.326530612 + 2.489795918t + t2 = 0 Move the constant term to the right: Add '6.326530612' to each side of the equation. -6.326530612 + 2.489795918t + 6.326530612 + t2 = 0 + 6.326530612 Reorder the terms: -6.326530612 + 6.326530612 + 2.489795918t + t2 = 0 + 6.326530612 Combine like terms: -6.326530612 + 6.326530612 = 0.000000000 0.000000000 + 2.489795918t + t2 = 0 + 6.326530612 2.489795918t + t2 = 0 + 6.326530612 Combine like terms: 0 + 6.326530612 = 6.326530612 2.489795918t + t2 = 6.326530612 The t term is 2.489795918t. Take half its coefficient (1.244897959). Square it (1.549770928) and add it to both sides. Add '1.549770928' to each side of the equation. 2.489795918t + 1.549770928 + t2 = 6.326530612 + 1.549770928 Reorder the terms: 1.549770928 + 2.489795918t + t2 = 6.326530612 + 1.549770928 Combine like terms: 6.326530612 + 1.549770928 = 7.87630154 1.549770928 + 2.489795918t + t2 = 7.87630154 Factor a perfect square on the left side: (t + 1.244897959)(t + 1.244897959) = 7.87630154 Calculate the square root of the right side: 2.806474931 Break this problem into two subproblems by setting (t + 1.244897959) equal to 2.806474931 and -2.806474931.Subproblem 1
t + 1.244897959 = 2.806474931 Simplifying t + 1.244897959 = 2.806474931 Reorder the terms: 1.244897959 + t = 2.806474931 Solving 1.244897959 + t = 2.806474931 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.244897959' to each side of the equation. 1.244897959 + -1.244897959 + t = 2.806474931 + -1.244897959 Combine like terms: 1.244897959 + -1.244897959 = 0.000000000 0.000000000 + t = 2.806474931 + -1.244897959 t = 2.806474931 + -1.244897959 Combine like terms: 2.806474931 + -1.244897959 = 1.561576972 t = 1.561576972 Simplifying t = 1.561576972Subproblem 2
t + 1.244897959 = -2.806474931 Simplifying t + 1.244897959 = -2.806474931 Reorder the terms: 1.244897959 + t = -2.806474931 Solving 1.244897959 + t = -2.806474931 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.244897959' to each side of the equation. 1.244897959 + -1.244897959 + t = -2.806474931 + -1.244897959 Combine like terms: 1.244897959 + -1.244897959 = 0.000000000 0.000000000 + t = -2.806474931 + -1.244897959 t = -2.806474931 + -1.244897959 Combine like terms: -2.806474931 + -1.244897959 = -4.05137289 t = -4.05137289 Simplifying t = -4.05137289Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.561576972, -4.05137289}
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