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Simplifying q(q + 4) = 4 Reorder the terms: q(4 + q) = 4 (4 * q + q * q) = 4 (4q + q2) = 4 Solving 4q + q2 = 4 Solving for variable 'q'. Reorder the terms: -4 + 4q + q2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 4q + q2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 4q + 4 + q2 = 0 + 4 Reorder the terms: -4 + 4 + 4q + q2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 4q + q2 = 0 + 4 4q + q2 = 0 + 4 Combine like terms: 0 + 4 = 4 4q + q2 = 4 The q term is 4q. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4q + 4 + q2 = 4 + 4 Reorder the terms: 4 + 4q + q2 = 4 + 4 Combine like terms: 4 + 4 = 8 4 + 4q + q2 = 8 Factor a perfect square on the left side: (q + 2)(q + 2) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (q + 2) equal to 2.828427125 and -2.828427125.Subproblem 1
q + 2 = 2.828427125 Simplifying q + 2 = 2.828427125 Reorder the terms: 2 + q = 2.828427125 Solving 2 + q = 2.828427125 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + q = 2.828427125 + -2 Combine like terms: 2 + -2 = 0 0 + q = 2.828427125 + -2 q = 2.828427125 + -2 Combine like terms: 2.828427125 + -2 = 0.828427125 q = 0.828427125 Simplifying q = 0.828427125Subproblem 2
q + 2 = -2.828427125 Simplifying q + 2 = -2.828427125 Reorder the terms: 2 + q = -2.828427125 Solving 2 + q = -2.828427125 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + q = -2.828427125 + -2 Combine like terms: 2 + -2 = 0 0 + q = -2.828427125 + -2 q = -2.828427125 + -2 Combine like terms: -2.828427125 + -2 = -4.828427125 q = -4.828427125 Simplifying q = -4.828427125Solution
The solution to the problem is based on the solutions from the subproblems. q = {0.828427125, -4.828427125}
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