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Simplifying q * q + 2q + -7 = 5 Multiply q * q q2 + 2q + -7 = 5 Reorder the terms: -7 + 2q + q2 = 5 Solving -7 + 2q + q2 = 5 Solving for variable 'q'. Reorder the terms: -7 + -5 + 2q + q2 = 5 + -5 Combine like terms: -7 + -5 = -12 -12 + 2q + q2 = 5 + -5 Combine like terms: 5 + -5 = 0 -12 + 2q + q2 = 0 Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + 2q + 12 + q2 = 0 + 12 Reorder the terms: -12 + 12 + 2q + q2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 2q + q2 = 0 + 12 2q + q2 = 0 + 12 Combine like terms: 0 + 12 = 12 2q + q2 = 12 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 = 12 + 1 Reorder the terms: 1 + 2q + q2 = 12 + 1 Combine like terms: 12 + 1 = 13 1 + 2q + q2 = 13 Factor a perfect square on the left side: (q + 1)(q + 1) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (q + 1) equal to 3.605551275 and -3.605551275.Subproblem 1
q + 1 = 3.605551275 Simplifying q + 1 = 3.605551275 Reorder the terms: 1 + q = 3.605551275 Solving 1 + q = 3.605551275 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 = 3.605551275 + -1 Combine like terms: 1 + -1 = 0 0 + q = 3.605551275 + -1 q = 3.605551275 + -1 Combine like terms: 3.605551275 + -1 = 2.605551275 q = 2.605551275 Simplifying q = 2.605551275Subproblem 2
q + 1 = -3.605551275 Simplifying q + 1 = -3.605551275 Reorder the terms: 1 + q = -3.605551275 Solving 1 + q = -3.605551275 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 = -3.605551275 + -1 Combine like terms: 1 + -1 = 0 0 + q = -3.605551275 + -1 q = -3.605551275 + -1 Combine like terms: -3.605551275 + -1 = -4.605551275 q = -4.605551275 Simplifying q = -4.605551275Solution
The solution to the problem is based on the solutions from the subproblems. q = {2.605551275, -4.605551275}
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