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Simplifying -7t2 + -7t + 4 = 0 Reorder the terms: 4 + -7t + -7t2 = 0 Solving 4 + -7t + -7t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -0.5714285714 + t + t2 = 0 Move the constant term to the right: Add '0.5714285714' to each side of the equation. -0.5714285714 + t + 0.5714285714 + t2 = 0 + 0.5714285714 Reorder the terms: -0.5714285714 + 0.5714285714 + t + t2 = 0 + 0.5714285714 Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000 0.0000000000 + t + t2 = 0 + 0.5714285714 t + t2 = 0 + 0.5714285714 Combine like terms: 0 + 0.5714285714 = 0.5714285714 t + t2 = 0.5714285714 The t term is t. 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. + 0.25 + t2 = 0.5714285714 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + t2 = 0.5714285714 + 0.25 Combine like terms: 0.5714285714 + 0.25 = 0.8214285714 1.25 + t2 = 0.8214285714 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = 0.8214285714 Calculate the square root of the right side: 0.906326967 Break this problem into two subproblems by setting (t + 0.5) equal to 0.906326967 and -0.906326967.Subproblem 1
t + 0.5 = 0.906326967 Simplifying t + 0.5 = 0.906326967 Reorder the terms: 0.5 + t = 0.906326967 Solving 0.5 + t = 0.906326967 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 = 0.906326967 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = 0.906326967 + -0.5 t = 0.906326967 + -0.5 Combine like terms: 0.906326967 + -0.5 = 0.406326967 t = 0.406326967 Simplifying t = 0.406326967Subproblem 2
t + 0.5 = -0.906326967 Simplifying t + 0.5 = -0.906326967 Reorder the terms: 0.5 + t = -0.906326967 Solving 0.5 + t = -0.906326967 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 = -0.906326967 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = -0.906326967 + -0.5 t = -0.906326967 + -0.5 Combine like terms: -0.906326967 + -0.5 = -1.406326967 t = -1.406326967 Simplifying t = -1.406326967Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.406326967, -1.406326967}
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