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Simplifying 4q2 + 3q2 = -4q + 18 Combine like terms: 4q2 + 3q2 = 7q2 7q2 = -4q + 18 Reorder the terms: 7q2 = 18 + -4q Solving 7q2 = 18 + -4q Solving for variable 'q'. Reorder the terms: -18 + 4q + 7q2 = 18 + -4q + -18 + 4q Reorder the terms: -18 + 4q + 7q2 = 18 + -18 + -4q + 4q Combine like terms: 18 + -18 = 0 -18 + 4q + 7q2 = 0 + -4q + 4q -18 + 4q + 7q2 = -4q + 4q Combine like terms: -4q + 4q = 0 -18 + 4q + 7q2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -2.571428571 + 0.5714285714q + q2 = 0 Move the constant term to the right: Add '2.571428571' to each side of the equation. -2.571428571 + 0.5714285714q + 2.571428571 + q2 = 0 + 2.571428571 Reorder the terms: -2.571428571 + 2.571428571 + 0.5714285714q + q2 = 0 + 2.571428571 Combine like terms: -2.571428571 + 2.571428571 = 0.000000000 0.000000000 + 0.5714285714q + q2 = 0 + 2.571428571 0.5714285714q + q2 = 0 + 2.571428571 Combine like terms: 0 + 2.571428571 = 2.571428571 0.5714285714q + q2 = 2.571428571 The q term is 0.5714285714q. Take half its coefficient (0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. 0.5714285714q + 0.08163265305 + q2 = 2.571428571 + 0.08163265305 Reorder the terms: 0.08163265305 + 0.5714285714q + q2 = 2.571428571 + 0.08163265305 Combine like terms: 2.571428571 + 0.08163265305 = 2.65306122405 0.08163265305 + 0.5714285714q + q2 = 2.65306122405 Factor a perfect square on the left side: (q + 0.2857142857)(q + 0.2857142857) = 2.65306122405 Calculate the square root of the right side: 1.628822036 Break this problem into two subproblems by setting (q + 0.2857142857) equal to 1.628822036 and -1.628822036.Subproblem 1
q + 0.2857142857 = 1.628822036 Simplifying q + 0.2857142857 = 1.628822036 Reorder the terms: 0.2857142857 + q = 1.628822036 Solving 0.2857142857 + q = 1.628822036 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + q = 1.628822036 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + q = 1.628822036 + -0.2857142857 q = 1.628822036 + -0.2857142857 Combine like terms: 1.628822036 + -0.2857142857 = 1.3431077503 q = 1.3431077503 Simplifying q = 1.3431077503Subproblem 2
q + 0.2857142857 = -1.628822036 Simplifying q + 0.2857142857 = -1.628822036 Reorder the terms: 0.2857142857 + q = -1.628822036 Solving 0.2857142857 + q = -1.628822036 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + q = -1.628822036 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + q = -1.628822036 + -0.2857142857 q = -1.628822036 + -0.2857142857 Combine like terms: -1.628822036 + -0.2857142857 = -1.9145363217 q = -1.9145363217 Simplifying q = -1.9145363217Solution
The solution to the problem is based on the solutions from the subproblems. q = {1.3431077503, -1.9145363217}
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