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Simplifying 0.0295t2 + -0.918t + 1.742 = 0 Reorder the terms: 1.742 + -0.918t + 0.0295t2 = 0 Solving 1.742 + -0.918t + 0.0295t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 0.0295 the coefficient of the squared term: Divide each side by '0.0295'. 59.05084746 + -31.11864407t + t2 = 0 Move the constant term to the right: Add '-59.05084746' to each side of the equation. 59.05084746 + -31.11864407t + -59.05084746 + t2 = 0 + -59.05084746 Reorder the terms: 59.05084746 + -59.05084746 + -31.11864407t + t2 = 0 + -59.05084746 Combine like terms: 59.05084746 + -59.05084746 = 0.00000000 0.00000000 + -31.11864407t + t2 = 0 + -59.05084746 -31.11864407t + t2 = 0 + -59.05084746 Combine like terms: 0 + -59.05084746 = -59.05084746 -31.11864407t + t2 = -59.05084746 The t term is -31.11864407t. Take half its coefficient (-15.55932204). Square it (242.0925023) and add it to both sides. Add '242.0925023' to each side of the equation. -31.11864407t + 242.0925023 + t2 = -59.05084746 + 242.0925023 Reorder the terms: 242.0925023 + -31.11864407t + t2 = -59.05084746 + 242.0925023 Combine like terms: -59.05084746 + 242.0925023 = 183.04165484 242.0925023 + -31.11864407t + t2 = 183.04165484 Factor a perfect square on the left side: (t + -15.55932204)(t + -15.55932204) = 183.04165484 Calculate the square root of the right side: 13.529288778 Break this problem into two subproblems by setting (t + -15.55932204) equal to 13.529288778 and -13.529288778.Subproblem 1
t + -15.55932204 = 13.529288778 Simplifying t + -15.55932204 = 13.529288778 Reorder the terms: -15.55932204 + t = 13.529288778 Solving -15.55932204 + t = 13.529288778 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '15.55932204' to each side of the equation. -15.55932204 + 15.55932204 + t = 13.529288778 + 15.55932204 Combine like terms: -15.55932204 + 15.55932204 = 0.00000000 0.00000000 + t = 13.529288778 + 15.55932204 t = 13.529288778 + 15.55932204 Combine like terms: 13.529288778 + 15.55932204 = 29.088610818 t = 29.088610818 Simplifying t = 29.088610818Subproblem 2
t + -15.55932204 = -13.529288778 Simplifying t + -15.55932204 = -13.529288778 Reorder the terms: -15.55932204 + t = -13.529288778 Solving -15.55932204 + t = -13.529288778 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '15.55932204' to each side of the equation. -15.55932204 + 15.55932204 + t = -13.529288778 + 15.55932204 Combine like terms: -15.55932204 + 15.55932204 = 0.00000000 0.00000000 + t = -13.529288778 + 15.55932204 t = -13.529288778 + 15.55932204 Combine like terms: -13.529288778 + 15.55932204 = 2.030033262 t = 2.030033262 Simplifying t = 2.030033262Solution
The solution to the problem is based on the solutions from the subproblems. t = {29.088610818, 2.030033262}
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