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Simplifying q2 + -1q + -58 = 0 Reorder the terms: -58 + -1q + q2 = 0 Solving -58 + -1q + q2 = 0 Solving for variable 'q'. Begin completing the square. Move the constant term to the right: Add '58' to each side of the equation. -58 + -1q + 58 + q2 = 0 + 58 Reorder the terms: -58 + 58 + -1q + q2 = 0 + 58 Combine like terms: -58 + 58 = 0 0 + -1q + q2 = 0 + 58 -1q + q2 = 0 + 58 Combine like terms: 0 + 58 = 58 -1q + q2 = 58 The q term is -1q. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1q + 0.25 + q2 = 58 + 0.25 Reorder the terms: 0.25 + -1q + q2 = 58 + 0.25 Combine like terms: 58 + 0.25 = 58.25 0.25 + -1q + q2 = 58.25 Factor a perfect square on the left side: (q + -0.5)(q + -0.5) = 58.25 Calculate the square root of the right side: 7.632168761 Break this problem into two subproblems by setting (q + -0.5) equal to 7.632168761 and -7.632168761.Subproblem 1
q + -0.5 = 7.632168761 Simplifying q + -0.5 = 7.632168761 Reorder the terms: -0.5 + q = 7.632168761 Solving -0.5 + q = 7.632168761 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + q = 7.632168761 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + q = 7.632168761 + 0.5 q = 7.632168761 + 0.5 Combine like terms: 7.632168761 + 0.5 = 8.132168761 q = 8.132168761 Simplifying q = 8.132168761Subproblem 2
q + -0.5 = -7.632168761 Simplifying q + -0.5 = -7.632168761 Reorder the terms: -0.5 + q = -7.632168761 Solving -0.5 + q = -7.632168761 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + q = -7.632168761 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + q = -7.632168761 + 0.5 q = -7.632168761 + 0.5 Combine like terms: -7.632168761 + 0.5 = -7.132168761 q = -7.132168761 Simplifying q = -7.132168761Solution
The solution to the problem is based on the solutions from the subproblems. q = {8.132168761, -7.132168761}
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