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Simplifying 10t + 4.6t2 = 15 Solving 10t + 4.6t2 = 15 Solving for variable 't'. Reorder the terms: -15 + 10t + 4.6t2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + 10t + 4.6t2 = 0 Begin completing the square. Divide all terms by 4.6 the coefficient of the squared term: Divide each side by '4.6'. -3.260869565 + 2.173913043t + t2 = 0 Move the constant term to the right: Add '3.260869565' to each side of the equation. -3.260869565 + 2.173913043t + 3.260869565 + t2 = 0 + 3.260869565 Reorder the terms: -3.260869565 + 3.260869565 + 2.173913043t + t2 = 0 + 3.260869565 Combine like terms: -3.260869565 + 3.260869565 = 0.000000000 0.000000000 + 2.173913043t + t2 = 0 + 3.260869565 2.173913043t + t2 = 0 + 3.260869565 Combine like terms: 0 + 3.260869565 = 3.260869565 2.173913043t + t2 = 3.260869565 The t term is 2.173913043t. Take half its coefficient (1.086956522). Square it (1.181474481) and add it to both sides. Add '1.181474481' to each side of the equation. 2.173913043t + 1.181474481 + t2 = 3.260869565 + 1.181474481 Reorder the terms: 1.181474481 + 2.173913043t + t2 = 3.260869565 + 1.181474481 Combine like terms: 3.260869565 + 1.181474481 = 4.442344046 1.181474481 + 2.173913043t + t2 = 4.442344046 Factor a perfect square on the left side: (t + 1.086956522)(t + 1.086956522) = 4.442344046 Calculate the square root of the right side: 2.107686895 Break this problem into two subproblems by setting (t + 1.086956522) equal to 2.107686895 and -2.107686895.Subproblem 1
t + 1.086956522 = 2.107686895 Simplifying t + 1.086956522 = 2.107686895 Reorder the terms: 1.086956522 + t = 2.107686895 Solving 1.086956522 + t = 2.107686895 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.086956522' to each side of the equation. 1.086956522 + -1.086956522 + t = 2.107686895 + -1.086956522 Combine like terms: 1.086956522 + -1.086956522 = 0.000000000 0.000000000 + t = 2.107686895 + -1.086956522 t = 2.107686895 + -1.086956522 Combine like terms: 2.107686895 + -1.086956522 = 1.020730373 t = 1.020730373 Simplifying t = 1.020730373Subproblem 2
t + 1.086956522 = -2.107686895 Simplifying t + 1.086956522 = -2.107686895 Reorder the terms: 1.086956522 + t = -2.107686895 Solving 1.086956522 + t = -2.107686895 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.086956522' to each side of the equation. 1.086956522 + -1.086956522 + t = -2.107686895 + -1.086956522 Combine like terms: 1.086956522 + -1.086956522 = 0.000000000 0.000000000 + t = -2.107686895 + -1.086956522 t = -2.107686895 + -1.086956522 Combine like terms: -2.107686895 + -1.086956522 = -3.194643417 t = -3.194643417 Simplifying t = -3.194643417Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.020730373, -3.194643417}
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