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Simplifying 7w2 + 6w + -9 = 0 Reorder the terms: -9 + 6w + 7w2 = 0 Solving -9 + 6w + 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 + 0.8571428571w + w2 = 0 Move the constant term to the right: Add '1.285714286' to each side of the equation. -1.285714286 + 0.8571428571w + 1.285714286 + w2 = 0 + 1.285714286 Reorder the terms: -1.285714286 + 1.285714286 + 0.8571428571w + w2 = 0 + 1.285714286 Combine like terms: -1.285714286 + 1.285714286 = 0.000000000 0.000000000 + 0.8571428571w + w2 = 0 + 1.285714286 0.8571428571w + w2 = 0 + 1.285714286 Combine like terms: 0 + 1.285714286 = 1.285714286 0.8571428571w + w2 = 1.285714286 The w term is 0.8571428571w. Take half its coefficient (0.4285714286). Square it (0.1836734694) and add it to both sides. Add '0.1836734694' to each side of the equation. 0.8571428571w + 0.1836734694 + w2 = 1.285714286 + 0.1836734694 Reorder the terms: 0.1836734694 + 0.8571428571w + w2 = 1.285714286 + 0.1836734694 Combine like terms: 1.285714286 + 0.1836734694 = 1.4693877554 0.1836734694 + 0.8571428571w + w2 = 1.4693877554 Factor a perfect square on the left side: (w + 0.4285714286)(w + 0.4285714286) = 1.4693877554 Calculate the square root of the right side: 1.212183054 Break this problem into two subproblems by setting (w + 0.4285714286) equal to 1.212183054 and -1.212183054.Subproblem 1
w + 0.4285714286 = 1.212183054 Simplifying w + 0.4285714286 = 1.212183054 Reorder the terms: 0.4285714286 + w = 1.212183054 Solving 0.4285714286 + w = 1.212183054 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.4285714286' to each side of the equation. 0.4285714286 + -0.4285714286 + w = 1.212183054 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + w = 1.212183054 + -0.4285714286 w = 1.212183054 + -0.4285714286 Combine like terms: 1.212183054 + -0.4285714286 = 0.7836116254 w = 0.7836116254 Simplifying w = 0.7836116254Subproblem 2
w + 0.4285714286 = -1.212183054 Simplifying w + 0.4285714286 = -1.212183054 Reorder the terms: 0.4285714286 + w = -1.212183054 Solving 0.4285714286 + w = -1.212183054 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.4285714286' to each side of the equation. 0.4285714286 + -0.4285714286 + w = -1.212183054 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + w = -1.212183054 + -0.4285714286 w = -1.212183054 + -0.4285714286 Combine like terms: -1.212183054 + -0.4285714286 = -1.6407544826 w = -1.6407544826 Simplifying w = -1.6407544826Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.7836116254, -1.6407544826}
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