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Simplifying 5q2 + -9q + -3 = 0 Reorder the terms: -3 + -9q + 5q2 = 0 Solving -3 + -9q + 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'. -0.6 + -1.8q + q2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -1.8q + 0.6 + q2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + -1.8q + q2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -1.8q + q2 = 0 + 0.6 -1.8q + q2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 -1.8q + q2 = 0.6 The q term is -1.8q. Take half its coefficient (-0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. -1.8q + 0.81 + q2 = 0.6 + 0.81 Reorder the terms: 0.81 + -1.8q + q2 = 0.6 + 0.81 Combine like terms: 0.6 + 0.81 = 1.41 0.81 + -1.8q + q2 = 1.41 Factor a perfect square on the left side: (q + -0.9)(q + -0.9) = 1.41 Calculate the square root of the right side: 1.187434209 Break this problem into two subproblems by setting (q + -0.9) equal to 1.187434209 and -1.187434209.Subproblem 1
q + -0.9 = 1.187434209 Simplifying q + -0.9 = 1.187434209 Reorder the terms: -0.9 + q = 1.187434209 Solving -0.9 + q = 1.187434209 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + q = 1.187434209 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + q = 1.187434209 + 0.9 q = 1.187434209 + 0.9 Combine like terms: 1.187434209 + 0.9 = 2.087434209 q = 2.087434209 Simplifying q = 2.087434209Subproblem 2
q + -0.9 = -1.187434209 Simplifying q + -0.9 = -1.187434209 Reorder the terms: -0.9 + q = -1.187434209 Solving -0.9 + q = -1.187434209 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + q = -1.187434209 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + q = -1.187434209 + 0.9 q = -1.187434209 + 0.9 Combine like terms: -1.187434209 + 0.9 = -0.287434209 q = -0.287434209 Simplifying q = -0.287434209Solution
The solution to the problem is based on the solutions from the subproblems. q = {2.087434209, -0.287434209}
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