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Simplifying 16t2 + -21t + -3 = 9 Reorder the terms: -3 + -21t + 16t2 = 9 Solving -3 + -21t + 16t2 = 9 Solving for variable 't'. Reorder the terms: -3 + -9 + -21t + 16t2 = 9 + -9 Combine like terms: -3 + -9 = -12 -12 + -21t + 16t2 = 9 + -9 Combine like terms: 9 + -9 = 0 -12 + -21t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.75 + -1.3125t + t2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -1.3125t + 0.75 + t2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -1.3125t + t2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -1.3125t + t2 = 0 + 0.75 -1.3125t + t2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -1.3125t + t2 = 0.75 The t term is -1.3125t. Take half its coefficient (-0.65625). Square it (0.4306640625) and add it to both sides. Add '0.4306640625' to each side of the equation. -1.3125t + 0.4306640625 + t2 = 0.75 + 0.4306640625 Reorder the terms: 0.4306640625 + -1.3125t + t2 = 0.75 + 0.4306640625 Combine like terms: 0.75 + 0.4306640625 = 1.1806640625 0.4306640625 + -1.3125t + t2 = 1.1806640625 Factor a perfect square on the left side: (t + -0.65625)(t + -0.65625) = 1.1806640625 Calculate the square root of the right side: 1.086583666 Break this problem into two subproblems by setting (t + -0.65625) equal to 1.086583666 and -1.086583666.Subproblem 1
t + -0.65625 = 1.086583666 Simplifying t + -0.65625 = 1.086583666 Reorder the terms: -0.65625 + t = 1.086583666 Solving -0.65625 + t = 1.086583666 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.65625' to each side of the equation. -0.65625 + 0.65625 + t = 1.086583666 + 0.65625 Combine like terms: -0.65625 + 0.65625 = 0.00000 0.00000 + t = 1.086583666 + 0.65625 t = 1.086583666 + 0.65625 Combine like terms: 1.086583666 + 0.65625 = 1.742833666 t = 1.742833666 Simplifying t = 1.742833666Subproblem 2
t + -0.65625 = -1.086583666 Simplifying t + -0.65625 = -1.086583666 Reorder the terms: -0.65625 + t = -1.086583666 Solving -0.65625 + t = -1.086583666 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.65625' to each side of the equation. -0.65625 + 0.65625 + t = -1.086583666 + 0.65625 Combine like terms: -0.65625 + 0.65625 = 0.00000 0.00000 + t = -1.086583666 + 0.65625 t = -1.086583666 + 0.65625 Combine like terms: -1.086583666 + 0.65625 = -0.430333666 t = -0.430333666 Simplifying t = -0.430333666Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.742833666, -0.430333666}
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