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Simplifying -16t2 + 15t + 3 = 0 Reorder the terms: 3 + 15t + -16t2 = 0 Solving 3 + 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'. -0.1875 + -0.9375t + t2 = 0 Move the constant term to the right: Add '0.1875' to each side of the equation. -0.1875 + -0.9375t + 0.1875 + t2 = 0 + 0.1875 Reorder the terms: -0.1875 + 0.1875 + -0.9375t + t2 = 0 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + -0.9375t + t2 = 0 + 0.1875 -0.9375t + t2 = 0 + 0.1875 Combine like terms: 0 + 0.1875 = 0.1875 -0.9375t + t2 = 0.1875 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 = 0.1875 + 0.2197265625 Reorder the terms: 0.2197265625 + -0.9375t + t2 = 0.1875 + 0.2197265625 Combine like terms: 0.1875 + 0.2197265625 = 0.4072265625 0.2197265625 + -0.9375t + t2 = 0.4072265625 Factor a perfect square on the left side: (t + -0.46875)(t + -0.46875) = 0.4072265625 Calculate the square root of the right side: 0.638143058 Break this problem into two subproblems by setting (t + -0.46875) equal to 0.638143058 and -0.638143058.Subproblem 1
t + -0.46875 = 0.638143058 Simplifying t + -0.46875 = 0.638143058 Reorder the terms: -0.46875 + t = 0.638143058 Solving -0.46875 + t = 0.638143058 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 = 0.638143058 + 0.46875 Combine like terms: -0.46875 + 0.46875 = 0.00000 0.00000 + t = 0.638143058 + 0.46875 t = 0.638143058 + 0.46875 Combine like terms: 0.638143058 + 0.46875 = 1.106893058 t = 1.106893058 Simplifying t = 1.106893058Subproblem 2
t + -0.46875 = -0.638143058 Simplifying t + -0.46875 = -0.638143058 Reorder the terms: -0.46875 + t = -0.638143058 Solving -0.46875 + t = -0.638143058 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 = -0.638143058 + 0.46875 Combine like terms: -0.46875 + 0.46875 = 0.00000 0.00000 + t = -0.638143058 + 0.46875 t = -0.638143058 + 0.46875 Combine like terms: -0.638143058 + 0.46875 = -0.169393058 t = -0.169393058 Simplifying t = -0.169393058Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.106893058, -0.169393058}
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