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Simplifying -5t2 + 13t + 2 = 0 Reorder the terms: 2 + 13t + -5t2 = 0 Solving 2 + 13t + -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'. -0.4 + -2.6t + t2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + -2.6t + 0.4 + t2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + -2.6t + t2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + -2.6t + t2 = 0 + 0.4 -2.6t + t2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 -2.6t + t2 = 0.4 The t term is -2.6t. Take half its coefficient (-1.3). Square it (1.69) and add it to both sides. Add '1.69' to each side of the equation. -2.6t + 1.69 + t2 = 0.4 + 1.69 Reorder the terms: 1.69 + -2.6t + t2 = 0.4 + 1.69 Combine like terms: 0.4 + 1.69 = 2.09 1.69 + -2.6t + t2 = 2.09 Factor a perfect square on the left side: (t + -1.3)(t + -1.3) = 2.09 Calculate the square root of the right side: 1.445683229 Break this problem into two subproblems by setting (t + -1.3) equal to 1.445683229 and -1.445683229.Subproblem 1
t + -1.3 = 1.445683229 Simplifying t + -1.3 = 1.445683229 Reorder the terms: -1.3 + t = 1.445683229 Solving -1.3 + t = 1.445683229 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.3' to each side of the equation. -1.3 + 1.3 + t = 1.445683229 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + t = 1.445683229 + 1.3 t = 1.445683229 + 1.3 Combine like terms: 1.445683229 + 1.3 = 2.745683229 t = 2.745683229 Simplifying t = 2.745683229Subproblem 2
t + -1.3 = -1.445683229 Simplifying t + -1.3 = -1.445683229 Reorder the terms: -1.3 + t = -1.445683229 Solving -1.3 + t = -1.445683229 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.3' to each side of the equation. -1.3 + 1.3 + t = -1.445683229 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + t = -1.445683229 + 1.3 t = -1.445683229 + 1.3 Combine like terms: -1.445683229 + 1.3 = -0.145683229 t = -0.145683229 Simplifying t = -0.145683229Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.745683229, -0.145683229}
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