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Simplifying 5q2 + -2q + -2 = 0 Reorder the terms: -2 + -2q + 5q2 = 0 Solving -2 + -2q + 5q2 = 0 Solving for variable 'q'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.4 + -0.4q + q2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + -0.4q + 0.4 + q2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + -0.4q + q2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + -0.4q + q2 = 0 + 0.4 -0.4q + q2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 -0.4q + q2 = 0.4 The q term is -0.4q. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4q + 0.04 + q2 = 0.4 + 0.04 Reorder the terms: 0.04 + -0.4q + q2 = 0.4 + 0.04 Combine like terms: 0.4 + 0.04 = 0.44 0.04 + -0.4q + q2 = 0.44 Factor a perfect square on the left side: (q + -0.2)(q + -0.2) = 0.44 Calculate the square root of the right side: 0.663324958 Break this problem into two subproblems by setting (q + -0.2) equal to 0.663324958 and -0.663324958.Subproblem 1
q + -0.2 = 0.663324958 Simplifying q + -0.2 = 0.663324958 Reorder the terms: -0.2 + q = 0.663324958 Solving -0.2 + q = 0.663324958 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + q = 0.663324958 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + q = 0.663324958 + 0.2 q = 0.663324958 + 0.2 Combine like terms: 0.663324958 + 0.2 = 0.863324958 q = 0.863324958 Simplifying q = 0.863324958Subproblem 2
q + -0.2 = -0.663324958 Simplifying q + -0.2 = -0.663324958 Reorder the terms: -0.2 + q = -0.663324958 Solving -0.2 + q = -0.663324958 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + q = -0.663324958 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + q = -0.663324958 + 0.2 q = -0.663324958 + 0.2 Combine like terms: -0.663324958 + 0.2 = -0.463324958 q = -0.463324958 Simplifying q = -0.463324958Solution
The solution to the problem is based on the solutions from the subproblems. q = {0.863324958, -0.463324958}
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