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Simplifying 5t2 = 3t + 28 Reorder the terms: 5t2 = 28 + 3t Solving 5t2 = 28 + 3t Solving for variable 't'. Reorder the terms: -28 + -3t + 5t2 = 28 + 3t + -28 + -3t Reorder the terms: -28 + -3t + 5t2 = 28 + -28 + 3t + -3t Combine like terms: 28 + -28 = 0 -28 + -3t + 5t2 = 0 + 3t + -3t -28 + -3t + 5t2 = 3t + -3t Combine like terms: 3t + -3t = 0 -28 + -3t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -5.6 + -0.6t + t2 = 0 Move the constant term to the right: Add '5.6' to each side of the equation. -5.6 + -0.6t + 5.6 + t2 = 0 + 5.6 Reorder the terms: -5.6 + 5.6 + -0.6t + t2 = 0 + 5.6 Combine like terms: -5.6 + 5.6 = 0.0 0.0 + -0.6t + t2 = 0 + 5.6 -0.6t + t2 = 0 + 5.6 Combine like terms: 0 + 5.6 = 5.6 -0.6t + t2 = 5.6 The t term is -0.6t. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6t + 0.09 + t2 = 5.6 + 0.09 Reorder the terms: 0.09 + -0.6t + t2 = 5.6 + 0.09 Combine like terms: 5.6 + 0.09 = 5.69 0.09 + -0.6t + t2 = 5.69 Factor a perfect square on the left side: (t + -0.3)(t + -0.3) = 5.69 Calculate the square root of the right side: 2.385372088 Break this problem into two subproblems by setting (t + -0.3) equal to 2.385372088 and -2.385372088.Subproblem 1
t + -0.3 = 2.385372088 Simplifying t + -0.3 = 2.385372088 Reorder the terms: -0.3 + t = 2.385372088 Solving -0.3 + t = 2.385372088 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + t = 2.385372088 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + t = 2.385372088 + 0.3 t = 2.385372088 + 0.3 Combine like terms: 2.385372088 + 0.3 = 2.685372088 t = 2.685372088 Simplifying t = 2.685372088Subproblem 2
t + -0.3 = -2.385372088 Simplifying t + -0.3 = -2.385372088 Reorder the terms: -0.3 + t = -2.385372088 Solving -0.3 + t = -2.385372088 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + t = -2.385372088 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + t = -2.385372088 + 0.3 t = -2.385372088 + 0.3 Combine like terms: -2.385372088 + 0.3 = -2.085372088 t = -2.085372088 Simplifying t = -2.085372088Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.685372088, -2.085372088}
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