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Simplifying 16t2 + -25t + 1 = 0 Reorder the terms: 1 + -25t + 16t2 = 0 Solving 1 + -25t + 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'. 0.0625 + -1.5625t + t2 = 0 Move the constant term to the right: Add '-0.0625' to each side of the equation. 0.0625 + -1.5625t + -0.0625 + t2 = 0 + -0.0625 Reorder the terms: 0.0625 + -0.0625 + -1.5625t + t2 = 0 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + -1.5625t + t2 = 0 + -0.0625 -1.5625t + t2 = 0 + -0.0625 Combine like terms: 0 + -0.0625 = -0.0625 -1.5625t + t2 = -0.0625 The t term is -1.5625t. Take half its coefficient (-0.78125). Square it (0.6103515625) and add it to both sides. Add '0.6103515625' to each side of the equation. -1.5625t + 0.6103515625 + t2 = -0.0625 + 0.6103515625 Reorder the terms: 0.6103515625 + -1.5625t + t2 = -0.0625 + 0.6103515625 Combine like terms: -0.0625 + 0.6103515625 = 0.5478515625 0.6103515625 + -1.5625t + t2 = 0.5478515625 Factor a perfect square on the left side: (t + -0.78125)(t + -0.78125) = 0.5478515625 Calculate the square root of the right side: 0.740169955 Break this problem into two subproblems by setting (t + -0.78125) equal to 0.740169955 and -0.740169955.Subproblem 1
t + -0.78125 = 0.740169955 Simplifying t + -0.78125 = 0.740169955 Reorder the terms: -0.78125 + t = 0.740169955 Solving -0.78125 + t = 0.740169955 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.78125' to each side of the equation. -0.78125 + 0.78125 + t = 0.740169955 + 0.78125 Combine like terms: -0.78125 + 0.78125 = 0.00000 0.00000 + t = 0.740169955 + 0.78125 t = 0.740169955 + 0.78125 Combine like terms: 0.740169955 + 0.78125 = 1.521419955 t = 1.521419955 Simplifying t = 1.521419955Subproblem 2
t + -0.78125 = -0.740169955 Simplifying t + -0.78125 = -0.740169955 Reorder the terms: -0.78125 + t = -0.740169955 Solving -0.78125 + t = -0.740169955 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.78125' to each side of the equation. -0.78125 + 0.78125 + t = -0.740169955 + 0.78125 Combine like terms: -0.78125 + 0.78125 = 0.00000 0.00000 + t = -0.740169955 + 0.78125 t = -0.740169955 + 0.78125 Combine like terms: -0.740169955 + 0.78125 = 0.041080045 t = 0.041080045 Simplifying t = 0.041080045Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.521419955, 0.041080045}
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