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Simplifying 25t2 + -25t + -3 = 0 Reorder the terms: -3 + -25t + 25t2 = 0 Solving -3 + -25t + 25t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.12 + -1t + t2 = 0 Move the constant term to the right: Add '0.12' to each side of the equation. -0.12 + -1t + 0.12 + t2 = 0 + 0.12 Reorder the terms: -0.12 + 0.12 + -1t + t2 = 0 + 0.12 Combine like terms: -0.12 + 0.12 = 0.00 0.00 + -1t + t2 = 0 + 0.12 -1t + t2 = 0 + 0.12 Combine like terms: 0 + 0.12 = 0.12 -1t + t2 = 0.12 The t term is -1t. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1t + 0.25 + t2 = 0.12 + 0.25 Reorder the terms: 0.25 + -1t + t2 = 0.12 + 0.25 Combine like terms: 0.12 + 0.25 = 0.37 0.25 + -1t + t2 = 0.37 Factor a perfect square on the left side: (t + -0.5)(t + -0.5) = 0.37 Calculate the square root of the right side: 0.608276253 Break this problem into two subproblems by setting (t + -0.5) equal to 0.608276253 and -0.608276253.Subproblem 1
t + -0.5 = 0.608276253 Simplifying t + -0.5 = 0.608276253 Reorder the terms: -0.5 + t = 0.608276253 Solving -0.5 + t = 0.608276253 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + t = 0.608276253 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = 0.608276253 + 0.5 t = 0.608276253 + 0.5 Combine like terms: 0.608276253 + 0.5 = 1.108276253 t = 1.108276253 Simplifying t = 1.108276253Subproblem 2
t + -0.5 = -0.608276253 Simplifying t + -0.5 = -0.608276253 Reorder the terms: -0.5 + t = -0.608276253 Solving -0.5 + t = -0.608276253 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + t = -0.608276253 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = -0.608276253 + 0.5 t = -0.608276253 + 0.5 Combine like terms: -0.608276253 + 0.5 = -0.108276253 t = -0.108276253 Simplifying t = -0.108276253Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.108276253, -0.108276253}
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