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Simplifying -5q2 + 9q + 6 = 0 Reorder the terms: 6 + 9q + -5q2 = 0 Solving 6 + 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'. -1.2 + -1.8q + q2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + -1.8q + 1.2 + q2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + -1.8q + q2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + -1.8q + q2 = 0 + 1.2 -1.8q + q2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 -1.8q + q2 = 1.2 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 = 1.2 + 0.81 Reorder the terms: 0.81 + -1.8q + q2 = 1.2 + 0.81 Combine like terms: 1.2 + 0.81 = 2.01 0.81 + -1.8q + q2 = 2.01 Factor a perfect square on the left side: (q + -0.9)(q + -0.9) = 2.01 Calculate the square root of the right side: 1.417744688 Break this problem into two subproblems by setting (q + -0.9) equal to 1.417744688 and -1.417744688.Subproblem 1
q + -0.9 = 1.417744688 Simplifying q + -0.9 = 1.417744688 Reorder the terms: -0.9 + q = 1.417744688 Solving -0.9 + q = 1.417744688 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 = 1.417744688 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + q = 1.417744688 + 0.9 q = 1.417744688 + 0.9 Combine like terms: 1.417744688 + 0.9 = 2.317744688 q = 2.317744688 Simplifying q = 2.317744688Subproblem 2
q + -0.9 = -1.417744688 Simplifying q + -0.9 = -1.417744688 Reorder the terms: -0.9 + q = -1.417744688 Solving -0.9 + q = -1.417744688 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 = -1.417744688 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + q = -1.417744688 + 0.9 q = -1.417744688 + 0.9 Combine like terms: -1.417744688 + 0.9 = -0.517744688 q = -0.517744688 Simplifying q = -0.517744688Solution
The solution to the problem is based on the solutions from the subproblems. q = {2.317744688, -0.517744688}
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