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Simplifying -10w * 11w + -7 + 4 = 7 * 11w + -7 Reorder the terms for easier multiplication: -10 * 11w * w + -7 + 4 = 7 * 11w + -7 Multiply -10 * 11 -110w * w + -7 + 4 = 7 * 11w + -7 Multiply w * w -110w2 + -7 + 4 = 7 * 11w + -7 Reorder the terms: -7 + 4 + -110w2 = 7 * 11w + -7 Combine like terms: -7 + 4 = -3 -3 + -110w2 = 7 * 11w + -7 Multiply 7 * 11 -3 + -110w2 = 77w + -7 Reorder the terms: -3 + -110w2 = -7 + 77w Solving -3 + -110w2 = -7 + 77w Solving for variable 'w'. Reorder the terms: -3 + 7 + -77w + -110w2 = -7 + 77w + 7 + -77w Combine like terms: -3 + 7 = 4 4 + -77w + -110w2 = -7 + 77w + 7 + -77w Reorder the terms: 4 + -77w + -110w2 = -7 + 7 + 77w + -77w Combine like terms: -7 + 7 = 0 4 + -77w + -110w2 = 0 + 77w + -77w 4 + -77w + -110w2 = 77w + -77w Combine like terms: 77w + -77w = 0 4 + -77w + -110w2 = 0 Begin completing the square. Divide all terms by -110 the coefficient of the squared term: Divide each side by '-110'. -0.03636363636 + 0.7w + w2 = 0.0 Move the constant term to the right: Add '0.03636363636' to each side of the equation. -0.03636363636 + 0.7w + 0.03636363636 + w2 = 0.0 + 0.03636363636 Reorder the terms: -0.03636363636 + 0.03636363636 + 0.7w + w2 = 0.0 + 0.03636363636 Combine like terms: -0.03636363636 + 0.03636363636 = 0.00000000000 0.00000000000 + 0.7w + w2 = 0.0 + 0.03636363636 0.7w + w2 = 0.0 + 0.03636363636 Combine like terms: 0.0 + 0.03636363636 = 0.03636363636 0.7w + w2 = 0.03636363636 The w term is 0.7w. Take half its coefficient (0.35). Square it (0.1225) and add it to both sides. Add '0.1225' to each side of the equation. 0.7w + 0.1225 + w2 = 0.03636363636 + 0.1225 Reorder the terms: 0.1225 + 0.7w + w2 = 0.03636363636 + 0.1225 Combine like terms: 0.03636363636 + 0.1225 = 0.15886363636 0.1225 + 0.7w + w2 = 0.15886363636 Factor a perfect square on the left side: (w + 0.35)(w + 0.35) = 0.15886363636 Calculate the square root of the right side: 0.398577014 Break this problem into two subproblems by setting (w + 0.35) equal to 0.398577014 and -0.398577014.Subproblem 1
w + 0.35 = 0.398577014 Simplifying w + 0.35 = 0.398577014 Reorder the terms: 0.35 + w = 0.398577014 Solving 0.35 + w = 0.398577014 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.35' to each side of the equation. 0.35 + -0.35 + w = 0.398577014 + -0.35 Combine like terms: 0.35 + -0.35 = 0.00 0.00 + w = 0.398577014 + -0.35 w = 0.398577014 + -0.35 Combine like terms: 0.398577014 + -0.35 = 0.048577014 w = 0.048577014 Simplifying w = 0.048577014Subproblem 2
w + 0.35 = -0.398577014 Simplifying w + 0.35 = -0.398577014 Reorder the terms: 0.35 + w = -0.398577014 Solving 0.35 + w = -0.398577014 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.35' to each side of the equation. 0.35 + -0.35 + w = -0.398577014 + -0.35 Combine like terms: 0.35 + -0.35 = 0.00 0.00 + w = -0.398577014 + -0.35 w = -0.398577014 + -0.35 Combine like terms: -0.398577014 + -0.35 = -0.748577014 w = -0.748577014 Simplifying w = -0.748577014Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.048577014, -0.748577014}
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