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Simplifying (-4t2 + 7t + -2) + (5t2 + 3t + 1) = 0 Reorder the terms: (-2 + 7t + -4t2) + (5t2 + 3t + 1) = 0 Remove parenthesis around (-2 + 7t + -4t2) -2 + 7t + -4t2 + (5t2 + 3t + 1) = 0 Reorder the terms: -2 + 7t + -4t2 + (1 + 3t + 5t2) = 0 Remove parenthesis around (1 + 3t + 5t2) -2 + 7t + -4t2 + 1 + 3t + 5t2 = 0 Reorder the terms: -2 + 1 + 7t + 3t + -4t2 + 5t2 = 0 Combine like terms: -2 + 1 = -1 -1 + 7t + 3t + -4t2 + 5t2 = 0 Combine like terms: 7t + 3t = 10t -1 + 10t + -4t2 + 5t2 = 0 Combine like terms: -4t2 + 5t2 = 1t2 -1 + 10t + 1t2 = 0 Solving -1 + 10t + 1t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + 10t + 1 + t2 = 0 + 1 Reorder the terms: -1 + 1 + 10t + t2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 10t + t2 = 0 + 1 10t + t2 = 0 + 1 Combine like terms: 0 + 1 = 1 10t + t2 = 1 The t term is 10t. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10t + 25 + t2 = 1 + 25 Reorder the terms: 25 + 10t + t2 = 1 + 25 Combine like terms: 1 + 25 = 26 25 + 10t + t2 = 26 Factor a perfect square on the left side: (t + 5)(t + 5) = 26 Calculate the square root of the right side: 5.099019514 Break this problem into two subproblems by setting (t + 5) equal to 5.099019514 and -5.099019514.Subproblem 1
t + 5 = 5.099019514 Simplifying t + 5 = 5.099019514 Reorder the terms: 5 + t = 5.099019514 Solving 5 + t = 5.099019514 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + t = 5.099019514 + -5 Combine like terms: 5 + -5 = 0 0 + t = 5.099019514 + -5 t = 5.099019514 + -5 Combine like terms: 5.099019514 + -5 = 0.099019514 t = 0.099019514 Simplifying t = 0.099019514Subproblem 2
t + 5 = -5.099019514 Simplifying t + 5 = -5.099019514 Reorder the terms: 5 + t = -5.099019514 Solving 5 + t = -5.099019514 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + t = -5.099019514 + -5 Combine like terms: 5 + -5 = 0 0 + t = -5.099019514 + -5 t = -5.099019514 + -5 Combine like terms: -5.099019514 + -5 = -10.099019514 t = -10.099019514 Simplifying t = -10.099019514Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.099019514, -10.099019514}
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