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Simplifying -4.92t2 + -3.4t + 10 = 0 Reorder the terms: 10 + -3.4t + -4.92t2 = 0 Solving 10 + -3.4t + -4.92t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -4.92 the coefficient of the squared term: Divide each side by '-4.92'. -2.032520325 + 0.6910569106t + t2 = 0 Move the constant term to the right: Add '2.032520325' to each side of the equation. -2.032520325 + 0.6910569106t + 2.032520325 + t2 = 0 + 2.032520325 Reorder the terms: -2.032520325 + 2.032520325 + 0.6910569106t + t2 = 0 + 2.032520325 Combine like terms: -2.032520325 + 2.032520325 = 0.000000000 0.000000000 + 0.6910569106t + t2 = 0 + 2.032520325 0.6910569106t + t2 = 0 + 2.032520325 Combine like terms: 0 + 2.032520325 = 2.032520325 0.6910569106t + t2 = 2.032520325 The t term is 0.6910569106t. Take half its coefficient (0.3455284553). Square it (0.1193899134) and add it to both sides. Add '0.1193899134' to each side of the equation. 0.6910569106t + 0.1193899134 + t2 = 2.032520325 + 0.1193899134 Reorder the terms: 0.1193899134 + 0.6910569106t + t2 = 2.032520325 + 0.1193899134 Combine like terms: 2.032520325 + 0.1193899134 = 2.1519102384 0.1193899134 + 0.6910569106t + t2 = 2.1519102384 Factor a perfect square on the left side: (t + 0.3455284553)(t + 0.3455284553) = 2.1519102384 Calculate the square root of the right side: 1.466939071 Break this problem into two subproblems by setting (t + 0.3455284553) equal to 1.466939071 and -1.466939071.Subproblem 1
t + 0.3455284553 = 1.466939071 Simplifying t + 0.3455284553 = 1.466939071 Reorder the terms: 0.3455284553 + t = 1.466939071 Solving 0.3455284553 + t = 1.466939071 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.3455284553' to each side of the equation. 0.3455284553 + -0.3455284553 + t = 1.466939071 + -0.3455284553 Combine like terms: 0.3455284553 + -0.3455284553 = 0.0000000000 0.0000000000 + t = 1.466939071 + -0.3455284553 t = 1.466939071 + -0.3455284553 Combine like terms: 1.466939071 + -0.3455284553 = 1.1214106157 t = 1.1214106157 Simplifying t = 1.1214106157Subproblem 2
t + 0.3455284553 = -1.466939071 Simplifying t + 0.3455284553 = -1.466939071 Reorder the terms: 0.3455284553 + t = -1.466939071 Solving 0.3455284553 + t = -1.466939071 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.3455284553' to each side of the equation. 0.3455284553 + -0.3455284553 + t = -1.466939071 + -0.3455284553 Combine like terms: 0.3455284553 + -0.3455284553 = 0.0000000000 0.0000000000 + t = -1.466939071 + -0.3455284553 t = -1.466939071 + -0.3455284553 Combine like terms: -1.466939071 + -0.3455284553 = -1.8124675263 t = -1.8124675263 Simplifying t = -1.8124675263Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.1214106157, -1.8124675263}
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