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Simplifying -5t2 + -5t + 67 = 0 Reorder the terms: 67 + -5t + -5t2 = 0 Solving 67 + -5t + -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'. -13.4 + t + t2 = 0 Move the constant term to the right: Add '13.4' to each side of the equation. -13.4 + t + 13.4 + t2 = 0 + 13.4 Reorder the terms: -13.4 + 13.4 + t + t2 = 0 + 13.4 Combine like terms: -13.4 + 13.4 = 0.0 0.0 + t + t2 = 0 + 13.4 t + t2 = 0 + 13.4 Combine like terms: 0 + 13.4 = 13.4 t + t2 = 13.4 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 = 13.4 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + t2 = 13.4 + 0.25 Combine like terms: 13.4 + 0.25 = 13.65 1.25 + t2 = 13.65 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = 13.65 Calculate the square root of the right side: 3.69459064 Break this problem into two subproblems by setting (t + 0.5) equal to 3.69459064 and -3.69459064.Subproblem 1
t + 0.5 = 3.69459064 Simplifying t + 0.5 = 3.69459064 Reorder the terms: 0.5 + t = 3.69459064 Solving 0.5 + t = 3.69459064 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 = 3.69459064 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = 3.69459064 + -0.5 t = 3.69459064 + -0.5 Combine like terms: 3.69459064 + -0.5 = 3.19459064 t = 3.19459064 Simplifying t = 3.19459064Subproblem 2
t + 0.5 = -3.69459064 Simplifying t + 0.5 = -3.69459064 Reorder the terms: 0.5 + t = -3.69459064 Solving 0.5 + t = -3.69459064 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 = -3.69459064 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = -3.69459064 + -0.5 t = -3.69459064 + -0.5 Combine like terms: -3.69459064 + -0.5 = -4.19459064 t = -4.19459064 Simplifying t = -4.19459064Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.19459064, -4.19459064}
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