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Simplifying q2 + 0.4q + -0.36 = 0 Reorder the terms: -0.36 + 0.4q + q2 = 0 Solving -0.36 + 0.4q + q2 = 0 Solving for variable 'q'. Begin completing the square. Move the constant term to the right: Add '0.36' to each side of the equation. -0.36 + 0.4q + 0.36 + q2 = 0 + 0.36 Reorder the terms: -0.36 + 0.36 + 0.4q + q2 = 0 + 0.36 Combine like terms: -0.36 + 0.36 = 0.00 0.00 + 0.4q + q2 = 0 + 0.36 0.4q + q2 = 0 + 0.36 Combine like terms: 0 + 0.36 = 0.36 0.4q + q2 = 0.36 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 = 0.36 + 0.04 Reorder the terms: 0.04 + 0.4q + q2 = 0.36 + 0.04 Combine like terms: 0.36 + 0.04 = 0.4 0.04 + 0.4q + q2 = 0.4 Factor a perfect square on the left side: (q + 0.2)(q + 0.2) = 0.4 Calculate the square root of the right side: 0.632455532 Break this problem into two subproblems by setting (q + 0.2) equal to 0.632455532 and -0.632455532.Subproblem 1
q + 0.2 = 0.632455532 Simplifying q + 0.2 = 0.632455532 Reorder the terms: 0.2 + q = 0.632455532 Solving 0.2 + q = 0.632455532 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 = 0.632455532 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + q = 0.632455532 + -0.2 q = 0.632455532 + -0.2 Combine like terms: 0.632455532 + -0.2 = 0.432455532 q = 0.432455532 Simplifying q = 0.432455532Subproblem 2
q + 0.2 = -0.632455532 Simplifying q + 0.2 = -0.632455532 Reorder the terms: 0.2 + q = -0.632455532 Solving 0.2 + q = -0.632455532 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 = -0.632455532 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + q = -0.632455532 + -0.2 q = -0.632455532 + -0.2 Combine like terms: -0.632455532 + -0.2 = -0.832455532 q = -0.832455532 Simplifying q = -0.832455532Solution
The solution to the problem is based on the solutions from the subproblems. q = {0.432455532, -0.832455532}
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