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Simplifying -5t2 + 56t + 5 = 0 Reorder the terms: 5 + 56t + -5t2 = 0 Solving 5 + 56t + -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 + -11.2t + t2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -11.2t + 1 + t2 = 0 + 1 Reorder the terms: -1 + 1 + -11.2t + t2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -11.2t + t2 = 0 + 1 -11.2t + t2 = 0 + 1 Combine like terms: 0 + 1 = 1 -11.2t + t2 = 1 The t term is -11.2t. Take half its coefficient (-5.6). Square it (31.36) and add it to both sides. Add '31.36' to each side of the equation. -11.2t + 31.36 + t2 = 1 + 31.36 Reorder the terms: 31.36 + -11.2t + t2 = 1 + 31.36 Combine like terms: 1 + 31.36 = 32.36 31.36 + -11.2t + t2 = 32.36 Factor a perfect square on the left side: (t + -5.6)(t + -5.6) = 32.36 Calculate the square root of the right side: 5.688585061 Break this problem into two subproblems by setting (t + -5.6) equal to 5.688585061 and -5.688585061.Subproblem 1
t + -5.6 = 5.688585061 Simplifying t + -5.6 = 5.688585061 Reorder the terms: -5.6 + t = 5.688585061 Solving -5.6 + t = 5.688585061 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.6' to each side of the equation. -5.6 + 5.6 + t = 5.688585061 + 5.6 Combine like terms: -5.6 + 5.6 = 0.0 0.0 + t = 5.688585061 + 5.6 t = 5.688585061 + 5.6 Combine like terms: 5.688585061 + 5.6 = 11.288585061 t = 11.288585061 Simplifying t = 11.288585061Subproblem 2
t + -5.6 = -5.688585061 Simplifying t + -5.6 = -5.688585061 Reorder the terms: -5.6 + t = -5.688585061 Solving -5.6 + t = -5.688585061 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.6' to each side of the equation. -5.6 + 5.6 + t = -5.688585061 + 5.6 Combine like terms: -5.6 + 5.6 = 0.0 0.0 + t = -5.688585061 + 5.6 t = -5.688585061 + 5.6 Combine like terms: -5.688585061 + 5.6 = -0.088585061 t = -0.088585061 Simplifying t = -0.088585061Solution
The solution to the problem is based on the solutions from the subproblems. t = {11.288585061, -0.088585061}
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