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Simplifying 0 = 7w2 + 30w + -22 Reorder the terms: 0 = -22 + 30w + 7w2 Solving 0 = -22 + 30w + 7w2 Solving for variable 'w'. Combine like terms: 0 + 22 = 22 22 + -30w + -7w2 = -22 + 30w + 7w2 + 22 + -30w + -7w2 Reorder the terms: 22 + -30w + -7w2 = -22 + 22 + 30w + -30w + 7w2 + -7w2 Combine like terms: -22 + 22 = 0 22 + -30w + -7w2 = 0 + 30w + -30w + 7w2 + -7w2 22 + -30w + -7w2 = 30w + -30w + 7w2 + -7w2 Combine like terms: 30w + -30w = 0 22 + -30w + -7w2 = 0 + 7w2 + -7w2 22 + -30w + -7w2 = 7w2 + -7w2 Combine like terms: 7w2 + -7w2 = 0 22 + -30w + -7w2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -3.142857143 + 4.285714286w + w2 = 0 Move the constant term to the right: Add '3.142857143' to each side of the equation. -3.142857143 + 4.285714286w + 3.142857143 + w2 = 0 + 3.142857143 Reorder the terms: -3.142857143 + 3.142857143 + 4.285714286w + w2 = 0 + 3.142857143 Combine like terms: -3.142857143 + 3.142857143 = 0.000000000 0.000000000 + 4.285714286w + w2 = 0 + 3.142857143 4.285714286w + w2 = 0 + 3.142857143 Combine like terms: 0 + 3.142857143 = 3.142857143 4.285714286w + w2 = 3.142857143 The w term is 4.285714286w. Take half its coefficient (2.142857143). Square it (4.591836735) and add it to both sides. Add '4.591836735' to each side of the equation. 4.285714286w + 4.591836735 + w2 = 3.142857143 + 4.591836735 Reorder the terms: 4.591836735 + 4.285714286w + w2 = 3.142857143 + 4.591836735 Combine like terms: 3.142857143 + 4.591836735 = 7.734693878 4.591836735 + 4.285714286w + w2 = 7.734693878 Factor a perfect square on the left side: (w + 2.142857143)(w + 2.142857143) = 7.734693878 Calculate the square root of the right side: 2.781131762 Break this problem into two subproblems by setting (w + 2.142857143) equal to 2.781131762 and -2.781131762.Subproblem 1
w + 2.142857143 = 2.781131762 Simplifying w + 2.142857143 = 2.781131762 Reorder the terms: 2.142857143 + w = 2.781131762 Solving 2.142857143 + w = 2.781131762 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2.142857143' to each side of the equation. 2.142857143 + -2.142857143 + w = 2.781131762 + -2.142857143 Combine like terms: 2.142857143 + -2.142857143 = 0.000000000 0.000000000 + w = 2.781131762 + -2.142857143 w = 2.781131762 + -2.142857143 Combine like terms: 2.781131762 + -2.142857143 = 0.638274619 w = 0.638274619 Simplifying w = 0.638274619Subproblem 2
w + 2.142857143 = -2.781131762 Simplifying w + 2.142857143 = -2.781131762 Reorder the terms: 2.142857143 + w = -2.781131762 Solving 2.142857143 + w = -2.781131762 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2.142857143' to each side of the equation. 2.142857143 + -2.142857143 + w = -2.781131762 + -2.142857143 Combine like terms: 2.142857143 + -2.142857143 = 0.000000000 0.000000000 + w = -2.781131762 + -2.142857143 w = -2.781131762 + -2.142857143 Combine like terms: -2.781131762 + -2.142857143 = -4.923988905 w = -4.923988905 Simplifying w = -4.923988905Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.638274619, -4.923988905}
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