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Simplifying 9w2 = 8w + 3 Reorder the terms: 9w2 = 3 + 8w Solving 9w2 = 3 + 8w Solving for variable 'w'. Reorder the terms: -3 + -8w + 9w2 = 3 + 8w + -3 + -8w Reorder the terms: -3 + -8w + 9w2 = 3 + -3 + 8w + -8w Combine like terms: 3 + -3 = 0 -3 + -8w + 9w2 = 0 + 8w + -8w -3 + -8w + 9w2 = 8w + -8w Combine like terms: 8w + -8w = 0 -3 + -8w + 9w2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.3333333333 + -0.8888888889w + w2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + -0.8888888889w + 0.3333333333 + w2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + -0.8888888889w + w2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + -0.8888888889w + w2 = 0 + 0.3333333333 -0.8888888889w + w2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 -0.8888888889w + w2 = 0.3333333333 The w term is -0.8888888889w. Take half its coefficient (-0.4444444445). Square it (0.1975308642) and add it to both sides. Add '0.1975308642' to each side of the equation. -0.8888888889w + 0.1975308642 + w2 = 0.3333333333 + 0.1975308642 Reorder the terms: 0.1975308642 + -0.8888888889w + w2 = 0.3333333333 + 0.1975308642 Combine like terms: 0.3333333333 + 0.1975308642 = 0.5308641975 0.1975308642 + -0.8888888889w + w2 = 0.5308641975 Factor a perfect square on the left side: (w + -0.4444444445)(w + -0.4444444445) = 0.5308641975 Calculate the square root of the right side: 0.72860428 Break this problem into two subproblems by setting (w + -0.4444444445) equal to 0.72860428 and -0.72860428.Subproblem 1
w + -0.4444444445 = 0.72860428 Simplifying w + -0.4444444445 = 0.72860428 Reorder the terms: -0.4444444445 + w = 0.72860428 Solving -0.4444444445 + w = 0.72860428 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.4444444445' to each side of the equation. -0.4444444445 + 0.4444444445 + w = 0.72860428 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + w = 0.72860428 + 0.4444444445 w = 0.72860428 + 0.4444444445 Combine like terms: 0.72860428 + 0.4444444445 = 1.1730487245 w = 1.1730487245 Simplifying w = 1.1730487245Subproblem 2
w + -0.4444444445 = -0.72860428 Simplifying w + -0.4444444445 = -0.72860428 Reorder the terms: -0.4444444445 + w = -0.72860428 Solving -0.4444444445 + w = -0.72860428 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.4444444445' to each side of the equation. -0.4444444445 + 0.4444444445 + w = -0.72860428 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + w = -0.72860428 + 0.4444444445 w = -0.72860428 + 0.4444444445 Combine like terms: -0.72860428 + 0.4444444445 = -0.2841598355 w = -0.2841598355 Simplifying w = -0.2841598355Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.1730487245, -0.2841598355}
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