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Simplifying 7w2 + -3w + -9 = 0 Reorder the terms: -9 + -3w + 7w2 = 0 Solving -9 + -3w + 7w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.285714286 + -0.4285714286w + w2 = 0 Move the constant term to the right: Add '1.285714286' to each side of the equation. -1.285714286 + -0.4285714286w + 1.285714286 + w2 = 0 + 1.285714286 Reorder the terms: -1.285714286 + 1.285714286 + -0.4285714286w + w2 = 0 + 1.285714286 Combine like terms: -1.285714286 + 1.285714286 = 0.000000000 0.000000000 + -0.4285714286w + w2 = 0 + 1.285714286 -0.4285714286w + w2 = 0 + 1.285714286 Combine like terms: 0 + 1.285714286 = 1.285714286 -0.4285714286w + w2 = 1.285714286 The w term is -0.4285714286w. 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. -0.4285714286w + 0.04591836735 + w2 = 1.285714286 + 0.04591836735 Reorder the terms: 0.04591836735 + -0.4285714286w + w2 = 1.285714286 + 0.04591836735 Combine like terms: 1.285714286 + 0.04591836735 = 1.33163265335 0.04591836735 + -0.4285714286w + w2 = 1.33163265335 Factor a perfect square on the left side: (w + -0.2142857143)(w + -0.2142857143) = 1.33163265335 Calculate the square root of the right side: 1.153963887 Break this problem into two subproblems by setting (w + -0.2142857143) equal to 1.153963887 and -1.153963887.Subproblem 1
w + -0.2142857143 = 1.153963887 Simplifying w + -0.2142857143 = 1.153963887 Reorder the terms: -0.2142857143 + w = 1.153963887 Solving -0.2142857143 + w = 1.153963887 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.2142857143' to each side of the equation. -0.2142857143 + 0.2142857143 + w = 1.153963887 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + w = 1.153963887 + 0.2142857143 w = 1.153963887 + 0.2142857143 Combine like terms: 1.153963887 + 0.2142857143 = 1.3682496013 w = 1.3682496013 Simplifying w = 1.3682496013Subproblem 2
w + -0.2142857143 = -1.153963887 Simplifying w + -0.2142857143 = -1.153963887 Reorder the terms: -0.2142857143 + w = -1.153963887 Solving -0.2142857143 + w = -1.153963887 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.2142857143' to each side of the equation. -0.2142857143 + 0.2142857143 + w = -1.153963887 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + w = -1.153963887 + 0.2142857143 w = -1.153963887 + 0.2142857143 Combine like terms: -1.153963887 + 0.2142857143 = -0.9396781727 w = -0.9396781727 Simplifying w = -0.9396781727Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.3682496013, -0.9396781727}
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