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Simplifying -16t2 + 15.2t + 1.7 = 0 Reorder the terms: 1.7 + 15.2t + -16t2 = 0 Solving 1.7 + 15.2t + -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'. -0.10625 + -0.95t + t2 = 0 Move the constant term to the right: Add '0.10625' to each side of the equation. -0.10625 + -0.95t + 0.10625 + t2 = 0 + 0.10625 Reorder the terms: -0.10625 + 0.10625 + -0.95t + t2 = 0 + 0.10625 Combine like terms: -0.10625 + 0.10625 = 0.00000 0.00000 + -0.95t + t2 = 0 + 0.10625 -0.95t + t2 = 0 + 0.10625 Combine like terms: 0 + 0.10625 = 0.10625 -0.95t + t2 = 0.10625 The t term is -0.95t. Take half its coefficient (-0.475). Square it (0.225625) and add it to both sides. Add '0.225625' to each side of the equation. -0.95t + 0.225625 + t2 = 0.10625 + 0.225625 Reorder the terms: 0.225625 + -0.95t + t2 = 0.10625 + 0.225625 Combine like terms: 0.10625 + 0.225625 = 0.331875 0.225625 + -0.95t + t2 = 0.331875 Factor a perfect square on the left side: (t + -0.475)(t + -0.475) = 0.331875 Calculate the square root of the right side: 0.576085931 Break this problem into two subproblems by setting (t + -0.475) equal to 0.576085931 and -0.576085931.Subproblem 1
t + -0.475 = 0.576085931 Simplifying t + -0.475 = 0.576085931 Reorder the terms: -0.475 + t = 0.576085931 Solving -0.475 + t = 0.576085931 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.475' to each side of the equation. -0.475 + 0.475 + t = 0.576085931 + 0.475 Combine like terms: -0.475 + 0.475 = 0.000 0.000 + t = 0.576085931 + 0.475 t = 0.576085931 + 0.475 Combine like terms: 0.576085931 + 0.475 = 1.051085931 t = 1.051085931 Simplifying t = 1.051085931Subproblem 2
t + -0.475 = -0.576085931 Simplifying t + -0.475 = -0.576085931 Reorder the terms: -0.475 + t = -0.576085931 Solving -0.475 + t = -0.576085931 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.475' to each side of the equation. -0.475 + 0.475 + t = -0.576085931 + 0.475 Combine like terms: -0.475 + 0.475 = 0.000 0.000 + t = -0.576085931 + 0.475 t = -0.576085931 + 0.475 Combine like terms: -0.576085931 + 0.475 = -0.101085931 t = -0.101085931 Simplifying t = -0.101085931Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.051085931, -0.101085931}
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