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Simplifying 5t2 + 2t + -1.3 = 0 Reorder the terms: -1.3 + 2t + 5t2 = 0 Solving -1.3 + 2t + 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'. -0.26 + 0.4t + t2 = 0 Move the constant term to the right: Add '0.26' to each side of the equation. -0.26 + 0.4t + 0.26 + t2 = 0 + 0.26 Reorder the terms: -0.26 + 0.26 + 0.4t + t2 = 0 + 0.26 Combine like terms: -0.26 + 0.26 = 0.00 0.00 + 0.4t + t2 = 0 + 0.26 0.4t + t2 = 0 + 0.26 Combine like terms: 0 + 0.26 = 0.26 0.4t + t2 = 0.26 The t term is 0.4t. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4t + 0.04 + t2 = 0.26 + 0.04 Reorder the terms: 0.04 + 0.4t + t2 = 0.26 + 0.04 Combine like terms: 0.26 + 0.04 = 0.3 0.04 + 0.4t + t2 = 0.3 Factor a perfect square on the left side: (t + 0.2)(t + 0.2) = 0.3 Calculate the square root of the right side: 0.547722558 Break this problem into two subproblems by setting (t + 0.2) equal to 0.547722558 and -0.547722558.Subproblem 1
t + 0.2 = 0.547722558 Simplifying t + 0.2 = 0.547722558 Reorder the terms: 0.2 + t = 0.547722558 Solving 0.2 + t = 0.547722558 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + t = 0.547722558 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + t = 0.547722558 + -0.2 t = 0.547722558 + -0.2 Combine like terms: 0.547722558 + -0.2 = 0.347722558 t = 0.347722558 Simplifying t = 0.347722558Subproblem 2
t + 0.2 = -0.547722558 Simplifying t + 0.2 = -0.547722558 Reorder the terms: 0.2 + t = -0.547722558 Solving 0.2 + t = -0.547722558 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + t = -0.547722558 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + t = -0.547722558 + -0.2 t = -0.547722558 + -0.2 Combine like terms: -0.547722558 + -0.2 = -0.747722558 t = -0.747722558 Simplifying t = -0.747722558Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.347722558, -0.747722558}
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