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Simplifying -16t2 + 18t + 7 = 10 Reorder the terms: 7 + 18t + -16t2 = 10 Solving 7 + 18t + -16t2 = 10 Solving for variable 't'. Reorder the terms: 7 + -10 + 18t + -16t2 = 10 + -10 Combine like terms: 7 + -10 = -3 -3 + 18t + -16t2 = 10 + -10 Combine like terms: 10 + -10 = 0 -3 + 18t + -16t2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 0.1875 + -1.125t + t2 = 0 Move the constant term to the right: Add '-0.1875' to each side of the equation. 0.1875 + -1.125t + -0.1875 + t2 = 0 + -0.1875 Reorder the terms: 0.1875 + -0.1875 + -1.125t + t2 = 0 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + -1.125t + t2 = 0 + -0.1875 -1.125t + t2 = 0 + -0.1875 Combine like terms: 0 + -0.1875 = -0.1875 -1.125t + t2 = -0.1875 The t term is -1.125t. Take half its coefficient (-0.5625). Square it (0.31640625) and add it to both sides. Add '0.31640625' to each side of the equation. -1.125t + 0.31640625 + t2 = -0.1875 + 0.31640625 Reorder the terms: 0.31640625 + -1.125t + t2 = -0.1875 + 0.31640625 Combine like terms: -0.1875 + 0.31640625 = 0.12890625 0.31640625 + -1.125t + t2 = 0.12890625 Factor a perfect square on the left side: (t + -0.5625)(t + -0.5625) = 0.12890625 Calculate the square root of the right side: 0.359035165 Break this problem into two subproblems by setting (t + -0.5625) equal to 0.359035165 and -0.359035165.Subproblem 1
t + -0.5625 = 0.359035165 Simplifying t + -0.5625 = 0.359035165 Reorder the terms: -0.5625 + t = 0.359035165 Solving -0.5625 + t = 0.359035165 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5625' to each side of the equation. -0.5625 + 0.5625 + t = 0.359035165 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + t = 0.359035165 + 0.5625 t = 0.359035165 + 0.5625 Combine like terms: 0.359035165 + 0.5625 = 0.921535165 t = 0.921535165 Simplifying t = 0.921535165Subproblem 2
t + -0.5625 = -0.359035165 Simplifying t + -0.5625 = -0.359035165 Reorder the terms: -0.5625 + t = -0.359035165 Solving -0.5625 + t = -0.359035165 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5625' to each side of the equation. -0.5625 + 0.5625 + t = -0.359035165 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + t = -0.359035165 + 0.5625 t = -0.359035165 + 0.5625 Combine like terms: -0.359035165 + 0.5625 = 0.203464835 t = 0.203464835 Simplifying t = 0.203464835Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.921535165, 0.203464835}
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