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Simplifying 5t(t + 15) + -3(t + 2) = 0 Reorder the terms: 5t(15 + t) + -3(t + 2) = 0 (15 * 5t + t * 5t) + -3(t + 2) = 0 (75t + 5t2) + -3(t + 2) = 0 Reorder the terms: 75t + 5t2 + -3(2 + t) = 0 75t + 5t2 + (2 * -3 + t * -3) = 0 75t + 5t2 + (-6 + -3t) = 0 Reorder the terms: -6 + 75t + -3t + 5t2 = 0 Combine like terms: 75t + -3t = 72t -6 + 72t + 5t2 = 0 Solving -6 + 72t + 5t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.2 + 14.4t + t2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + 14.4t + 1.2 + t2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + 14.4t + t2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + 14.4t + t2 = 0 + 1.2 14.4t + t2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 14.4t + t2 = 1.2 The t term is 14.4t. Take half its coefficient (7.2). Square it (51.84) and add it to both sides. Add '51.84' to each side of the equation. 14.4t + 51.84 + t2 = 1.2 + 51.84 Reorder the terms: 51.84 + 14.4t + t2 = 1.2 + 51.84 Combine like terms: 1.2 + 51.84 = 53.04 51.84 + 14.4t + t2 = 53.04 Factor a perfect square on the left side: (t + 7.2)(t + 7.2) = 53.04 Calculate the square root of the right side: 7.282856582 Break this problem into two subproblems by setting (t + 7.2) equal to 7.282856582 and -7.282856582.Subproblem 1
t + 7.2 = 7.282856582 Simplifying t + 7.2 = 7.282856582 Reorder the terms: 7.2 + t = 7.282856582 Solving 7.2 + t = 7.282856582 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-7.2' to each side of the equation. 7.2 + -7.2 + t = 7.282856582 + -7.2 Combine like terms: 7.2 + -7.2 = 0.0 0.0 + t = 7.282856582 + -7.2 t = 7.282856582 + -7.2 Combine like terms: 7.282856582 + -7.2 = 0.082856582 t = 0.082856582 Simplifying t = 0.082856582Subproblem 2
t + 7.2 = -7.282856582 Simplifying t + 7.2 = -7.282856582 Reorder the terms: 7.2 + t = -7.282856582 Solving 7.2 + t = -7.282856582 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-7.2' to each side of the equation. 7.2 + -7.2 + t = -7.282856582 + -7.2 Combine like terms: 7.2 + -7.2 = 0.0 0.0 + t = -7.282856582 + -7.2 t = -7.282856582 + -7.2 Combine like terms: -7.282856582 + -7.2 = -14.482856582 t = -14.482856582 Simplifying t = -14.482856582Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.082856582, -14.482856582}
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