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Simplifying q2 + 2q + -49 = 0 Reorder the terms: -49 + 2q + q2 = 0 Solving -49 + 2q + q2 = 0 Solving for variable 'q'. Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + 2q + 49 + q2 = 0 + 49 Reorder the terms: -49 + 49 + 2q + q2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + 2q + q2 = 0 + 49 2q + q2 = 0 + 49 Combine like terms: 0 + 49 = 49 2q + q2 = 49 The q term is 2q. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2q + 1 + q2 = 49 + 1 Reorder the terms: 1 + 2q + q2 = 49 + 1 Combine like terms: 49 + 1 = 50 1 + 2q + q2 = 50 Factor a perfect square on the left side: (q + 1)(q + 1) = 50 Calculate the square root of the right side: 7.071067812 Break this problem into two subproblems by setting (q + 1) equal to 7.071067812 and -7.071067812.Subproblem 1
q + 1 = 7.071067812 Simplifying q + 1 = 7.071067812 Reorder the terms: 1 + q = 7.071067812 Solving 1 + q = 7.071067812 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + q = 7.071067812 + -1 Combine like terms: 1 + -1 = 0 0 + q = 7.071067812 + -1 q = 7.071067812 + -1 Combine like terms: 7.071067812 + -1 = 6.071067812 q = 6.071067812 Simplifying q = 6.071067812Subproblem 2
q + 1 = -7.071067812 Simplifying q + 1 = -7.071067812 Reorder the terms: 1 + q = -7.071067812 Solving 1 + q = -7.071067812 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + q = -7.071067812 + -1 Combine like terms: 1 + -1 = 0 0 + q = -7.071067812 + -1 q = -7.071067812 + -1 Combine like terms: -7.071067812 + -1 = -8.071067812 q = -8.071067812 Simplifying q = -8.071067812Solution
The solution to the problem is based on the solutions from the subproblems. q = {6.071067812, -8.071067812}
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