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Simplifying 16t2 + 15t + -151 = 0 Reorder the terms: -151 + 15t + 16t2 = 0 Solving -151 + 15t + 16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -9.4375 + 0.9375t + t2 = 0 Move the constant term to the right: Add '9.4375' to each side of the equation. -9.4375 + 0.9375t + 9.4375 + t2 = 0 + 9.4375 Reorder the terms: -9.4375 + 9.4375 + 0.9375t + t2 = 0 + 9.4375 Combine like terms: -9.4375 + 9.4375 = 0.0000 0.0000 + 0.9375t + t2 = 0 + 9.4375 0.9375t + t2 = 0 + 9.4375 Combine like terms: 0 + 9.4375 = 9.4375 0.9375t + t2 = 9.4375 The t term is 0.9375t. Take half its coefficient (0.46875). Square it (0.2197265625) and add it to both sides. Add '0.2197265625' to each side of the equation. 0.9375t + 0.2197265625 + t2 = 9.4375 + 0.2197265625 Reorder the terms: 0.2197265625 + 0.9375t + t2 = 9.4375 + 0.2197265625 Combine like terms: 9.4375 + 0.2197265625 = 9.6572265625 0.2197265625 + 0.9375t + t2 = 9.6572265625 Factor a perfect square on the left side: (t + 0.46875)(t + 0.46875) = 9.6572265625 Calculate the square root of the right side: 3.107607852 Break this problem into two subproblems by setting (t + 0.46875) equal to 3.107607852 and -3.107607852.Subproblem 1
t + 0.46875 = 3.107607852 Simplifying t + 0.46875 = 3.107607852 Reorder the terms: 0.46875 + t = 3.107607852 Solving 0.46875 + t = 3.107607852 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.46875' to each side of the equation. 0.46875 + -0.46875 + t = 3.107607852 + -0.46875 Combine like terms: 0.46875 + -0.46875 = 0.00000 0.00000 + t = 3.107607852 + -0.46875 t = 3.107607852 + -0.46875 Combine like terms: 3.107607852 + -0.46875 = 2.638857852 t = 2.638857852 Simplifying t = 2.638857852Subproblem 2
t + 0.46875 = -3.107607852 Simplifying t + 0.46875 = -3.107607852 Reorder the terms: 0.46875 + t = -3.107607852 Solving 0.46875 + t = -3.107607852 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.46875' to each side of the equation. 0.46875 + -0.46875 + t = -3.107607852 + -0.46875 Combine like terms: 0.46875 + -0.46875 = 0.00000 0.00000 + t = -3.107607852 + -0.46875 t = -3.107607852 + -0.46875 Combine like terms: -3.107607852 + -0.46875 = -3.576357852 t = -3.576357852 Simplifying t = -3.576357852Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.638857852, -3.576357852}
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