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Simplifying 9 = 16t2 + 26t + 4 Reorder the terms: 9 = 4 + 26t + 16t2 Solving 9 = 4 + 26t + 16t2 Solving for variable 't'. Combine like terms: 9 + -4 = 5 5 + -26t + -16t2 = 4 + 26t + 16t2 + -4 + -26t + -16t2 Reorder the terms: 5 + -26t + -16t2 = 4 + -4 + 26t + -26t + 16t2 + -16t2 Combine like terms: 4 + -4 = 0 5 + -26t + -16t2 = 0 + 26t + -26t + 16t2 + -16t2 5 + -26t + -16t2 = 26t + -26t + 16t2 + -16t2 Combine like terms: 26t + -26t = 0 5 + -26t + -16t2 = 0 + 16t2 + -16t2 5 + -26t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 5 + -26t + -16t2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.3125 + 1.625t + t2 = 0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + 1.625t + 0.3125 + t2 = 0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + 1.625t + t2 = 0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + 1.625t + t2 = 0 + 0.3125 1.625t + t2 = 0 + 0.3125 Combine like terms: 0 + 0.3125 = 0.3125 1.625t + t2 = 0.3125 The t term is 1.625t. Take half its coefficient (0.8125). Square it (0.66015625) and add it to both sides. Add '0.66015625' to each side of the equation. 1.625t + 0.66015625 + t2 = 0.3125 + 0.66015625 Reorder the terms: 0.66015625 + 1.625t + t2 = 0.3125 + 0.66015625 Combine like terms: 0.3125 + 0.66015625 = 0.97265625 0.66015625 + 1.625t + t2 = 0.97265625 Factor a perfect square on the left side: (t + 0.8125)(t + 0.8125) = 0.97265625 Calculate the square root of the right side: 0.986233365 Break this problem into two subproblems by setting (t + 0.8125) equal to 0.986233365 and -0.986233365.Subproblem 1
t + 0.8125 = 0.986233365 Simplifying t + 0.8125 = 0.986233365 Reorder the terms: 0.8125 + t = 0.986233365 Solving 0.8125 + t = 0.986233365 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.8125' to each side of the equation. 0.8125 + -0.8125 + t = 0.986233365 + -0.8125 Combine like terms: 0.8125 + -0.8125 = 0.0000 0.0000 + t = 0.986233365 + -0.8125 t = 0.986233365 + -0.8125 Combine like terms: 0.986233365 + -0.8125 = 0.173733365 t = 0.173733365 Simplifying t = 0.173733365Subproblem 2
t + 0.8125 = -0.986233365 Simplifying t + 0.8125 = -0.986233365 Reorder the terms: 0.8125 + t = -0.986233365 Solving 0.8125 + t = -0.986233365 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.8125' to each side of the equation. 0.8125 + -0.8125 + t = -0.986233365 + -0.8125 Combine like terms: 0.8125 + -0.8125 = 0.0000 0.0000 + t = -0.986233365 + -0.8125 t = -0.986233365 + -0.8125 Combine like terms: -0.986233365 + -0.8125 = -1.798733365 t = -1.798733365 Simplifying t = -1.798733365Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.173733365, -1.798733365}
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