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Simplifying 5t2 + -1.2t + -6 = 0 Reorder the terms: -6 + -1.2t + 5t2 = 0 Solving -6 + -1.2t + 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'. -1.2 + -0.24t + t2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + -0.24t + 1.2 + t2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + -0.24t + t2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + -0.24t + t2 = 0 + 1.2 -0.24t + t2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 -0.24t + t2 = 1.2 The t term is -0.24t. Take half its coefficient (-0.12). Square it (0.0144) and add it to both sides. Add '0.0144' to each side of the equation. -0.24t + 0.0144 + t2 = 1.2 + 0.0144 Reorder the terms: 0.0144 + -0.24t + t2 = 1.2 + 0.0144 Combine like terms: 1.2 + 0.0144 = 1.2144 0.0144 + -0.24t + t2 = 1.2144 Factor a perfect square on the left side: (t + -0.12)(t + -0.12) = 1.2144 Calculate the square root of the right side: 1.101998185 Break this problem into two subproblems by setting (t + -0.12) equal to 1.101998185 and -1.101998185.Subproblem 1
t + -0.12 = 1.101998185 Simplifying t + -0.12 = 1.101998185 Reorder the terms: -0.12 + t = 1.101998185 Solving -0.12 + t = 1.101998185 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.12' to each side of the equation. -0.12 + 0.12 + t = 1.101998185 + 0.12 Combine like terms: -0.12 + 0.12 = 0.00 0.00 + t = 1.101998185 + 0.12 t = 1.101998185 + 0.12 Combine like terms: 1.101998185 + 0.12 = 1.221998185 t = 1.221998185 Simplifying t = 1.221998185Subproblem 2
t + -0.12 = -1.101998185 Simplifying t + -0.12 = -1.101998185 Reorder the terms: -0.12 + t = -1.101998185 Solving -0.12 + t = -1.101998185 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.12' to each side of the equation. -0.12 + 0.12 + t = -1.101998185 + 0.12 Combine like terms: -0.12 + 0.12 = 0.00 0.00 + t = -1.101998185 + 0.12 t = -1.101998185 + 0.12 Combine like terms: -1.101998185 + 0.12 = -0.981998185 t = -0.981998185 Simplifying t = -0.981998185Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.221998185, -0.981998185}
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