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Simplifying q2 + q + -3 = 0 Reorder the terms: -3 + q + q2 = 0 Solving -3 + q + q2 = 0 Solving for variable 'q'. Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + q + 3 + q2 = 0 + 3 Reorder the terms: -3 + 3 + q + q2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + q + q2 = 0 + 3 q + q2 = 0 + 3 Combine like terms: 0 + 3 = 3 q + q2 = 3 The q term is q. 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. q + 0.25 + q2 = 3 + 0.25 Reorder the terms: 0.25 + q + q2 = 3 + 0.25 Combine like terms: 3 + 0.25 = 3.25 0.25 + q + q2 = 3.25 Factor a perfect square on the left side: (q + 0.5)(q + 0.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (q + 0.5) equal to 1.802775638 and -1.802775638.Subproblem 1
q + 0.5 = 1.802775638 Simplifying q + 0.5 = 1.802775638 Reorder the terms: 0.5 + q = 1.802775638 Solving 0.5 + q = 1.802775638 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 = 1.802775638 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + q = 1.802775638 + -0.5 q = 1.802775638 + -0.5 Combine like terms: 1.802775638 + -0.5 = 1.302775638 q = 1.302775638 Simplifying q = 1.302775638Subproblem 2
q + 0.5 = -1.802775638 Simplifying q + 0.5 = -1.802775638 Reorder the terms: 0.5 + q = -1.802775638 Solving 0.5 + q = -1.802775638 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 = -1.802775638 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + q = -1.802775638 + -0.5 q = -1.802775638 + -0.5 Combine like terms: -1.802775638 + -0.5 = -2.302775638 q = -2.302775638 Simplifying q = -2.302775638Solution
The solution to the problem is based on the solutions from the subproblems. q = {1.302775638, -2.302775638}
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