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Simplifying 5t2 + -10t + -8 = 0 Reorder the terms: -8 + -10t + 5t2 = 0 Solving -8 + -10t + 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'. -1.6 + -2t + t2 = 0 Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + -2t + 1.6 + t2 = 0 + 1.6 Reorder the terms: -1.6 + 1.6 + -2t + t2 = 0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + -2t + t2 = 0 + 1.6 -2t + t2 = 0 + 1.6 Combine like terms: 0 + 1.6 = 1.6 -2t + t2 = 1.6 The t term is -2t. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2t + 1 + t2 = 1.6 + 1 Reorder the terms: 1 + -2t + t2 = 1.6 + 1 Combine like terms: 1.6 + 1 = 2.6 1 + -2t + t2 = 2.6 Factor a perfect square on the left side: (t + -1)(t + -1) = 2.6 Calculate the square root of the right side: 1.61245155 Break this problem into two subproblems by setting (t + -1) equal to 1.61245155 and -1.61245155.Subproblem 1
t + -1 = 1.61245155 Simplifying t + -1 = 1.61245155 Reorder the terms: -1 + t = 1.61245155 Solving -1 + t = 1.61245155 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + t = 1.61245155 + 1 Combine like terms: -1 + 1 = 0 0 + t = 1.61245155 + 1 t = 1.61245155 + 1 Combine like terms: 1.61245155 + 1 = 2.61245155 t = 2.61245155 Simplifying t = 2.61245155Subproblem 2
t + -1 = -1.61245155 Simplifying t + -1 = -1.61245155 Reorder the terms: -1 + t = -1.61245155 Solving -1 + t = -1.61245155 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + t = -1.61245155 + 1 Combine like terms: -1 + 1 = 0 0 + t = -1.61245155 + 1 t = -1.61245155 + 1 Combine like terms: -1.61245155 + 1 = -0.61245155 t = -0.61245155 Simplifying t = -0.61245155Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.61245155, -0.61245155}
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