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Simplifying 10 + -2q + -1(q * q) = 0 Multiply q * q 10 + -2q + -1(q2) = 0 Solving 10 + -2q + -1q2 = 0 Solving for variable 'q'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -10 + 2q + q2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + 2q + 10 + q2 = 0 + 10 Reorder the terms: -10 + 10 + 2q + q2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 2q + q2 = 0 + 10 2q + q2 = 0 + 10 Combine like terms: 0 + 10 = 10 2q + q2 = 10 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 = 10 + 1 Reorder the terms: 1 + 2q + q2 = 10 + 1 Combine like terms: 10 + 1 = 11 1 + 2q + q2 = 11 Factor a perfect square on the left side: (q + 1)(q + 1) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (q + 1) equal to 3.31662479 and -3.31662479.Subproblem 1
q + 1 = 3.31662479 Simplifying q + 1 = 3.31662479 Reorder the terms: 1 + q = 3.31662479 Solving 1 + q = 3.31662479 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 = 3.31662479 + -1 Combine like terms: 1 + -1 = 0 0 + q = 3.31662479 + -1 q = 3.31662479 + -1 Combine like terms: 3.31662479 + -1 = 2.31662479 q = 2.31662479 Simplifying q = 2.31662479Subproblem 2
q + 1 = -3.31662479 Simplifying q + 1 = -3.31662479 Reorder the terms: 1 + q = -3.31662479 Solving 1 + q = -3.31662479 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 = -3.31662479 + -1 Combine like terms: 1 + -1 = 0 0 + q = -3.31662479 + -1 q = -3.31662479 + -1 Combine like terms: -3.31662479 + -1 = -4.31662479 q = -4.31662479 Simplifying q = -4.31662479Solution
The solution to the problem is based on the solutions from the subproblems. q = {2.31662479, -4.31662479}
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