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Simplifying -7q2 + -3q + 8 = 0 Reorder the terms: 8 + -3q + -7q2 = 0 Solving 8 + -3q + -7q2 = 0 Solving for variable 'q'. Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -1.142857143 + 0.4285714286q + q2 = 0 Move the constant term to the right: Add '1.142857143' to each side of the equation. -1.142857143 + 0.4285714286q + 1.142857143 + q2 = 0 + 1.142857143 Reorder the terms: -1.142857143 + 1.142857143 + 0.4285714286q + q2 = 0 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + 0.4285714286q + q2 = 0 + 1.142857143 0.4285714286q + q2 = 0 + 1.142857143 Combine like terms: 0 + 1.142857143 = 1.142857143 0.4285714286q + q2 = 1.142857143 The q term is 0.4285714286q. Take half its coefficient (0.2142857143). Square it (0.04591836735) and add it to both sides. Add '0.04591836735' to each side of the equation. 0.4285714286q + 0.04591836735 + q2 = 1.142857143 + 0.04591836735 Reorder the terms: 0.04591836735 + 0.4285714286q + q2 = 1.142857143 + 0.04591836735 Combine like terms: 1.142857143 + 0.04591836735 = 1.18877551035 0.04591836735 + 0.4285714286q + q2 = 1.18877551035 Factor a perfect square on the left side: (q + 0.2142857143)(q + 0.2142857143) = 1.18877551035 Calculate the square root of the right side: 1.090309823 Break this problem into two subproblems by setting (q + 0.2142857143) equal to 1.090309823 and -1.090309823.Subproblem 1
q + 0.2142857143 = 1.090309823 Simplifying q + 0.2142857143 = 1.090309823 Reorder the terms: 0.2142857143 + q = 1.090309823 Solving 0.2142857143 + q = 1.090309823 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.2142857143 + q = 1.090309823 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + q = 1.090309823 + -0.2142857143 q = 1.090309823 + -0.2142857143 Combine like terms: 1.090309823 + -0.2142857143 = 0.8760241087 q = 0.8760241087 Simplifying q = 0.8760241087Subproblem 2
q + 0.2142857143 = -1.090309823 Simplifying q + 0.2142857143 = -1.090309823 Reorder the terms: 0.2142857143 + q = -1.090309823 Solving 0.2142857143 + q = -1.090309823 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.2142857143 + q = -1.090309823 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + q = -1.090309823 + -0.2142857143 q = -1.090309823 + -0.2142857143 Combine like terms: -1.090309823 + -0.2142857143 = -1.3045955373 q = -1.3045955373 Simplifying q = -1.3045955373Solution
The solution to the problem is based on the solutions from the subproblems. q = {0.8760241087, -1.3045955373}
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