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Simplifying 5w2 + -3w + -50 = 0 Reorder the terms: -50 + -3w + 5w2 = 0 Solving -50 + -3w + 5w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -10 + -0.6w + w2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -0.6w + 10 + w2 = 0 + 10 Reorder the terms: -10 + 10 + -0.6w + w2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -0.6w + w2 = 0 + 10 -0.6w + w2 = 0 + 10 Combine like terms: 0 + 10 = 10 -0.6w + w2 = 10 The w term is -0.6w. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6w + 0.09 + w2 = 10 + 0.09 Reorder the terms: 0.09 + -0.6w + w2 = 10 + 0.09 Combine like terms: 10 + 0.09 = 10.09 0.09 + -0.6w + w2 = 10.09 Factor a perfect square on the left side: (w + -0.3)(w + -0.3) = 10.09 Calculate the square root of the right side: 3.176476035 Break this problem into two subproblems by setting (w + -0.3) equal to 3.176476035 and -3.176476035.Subproblem 1
w + -0.3 = 3.176476035 Simplifying w + -0.3 = 3.176476035 Reorder the terms: -0.3 + w = 3.176476035 Solving -0.3 + w = 3.176476035 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + w = 3.176476035 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + w = 3.176476035 + 0.3 w = 3.176476035 + 0.3 Combine like terms: 3.176476035 + 0.3 = 3.476476035 w = 3.476476035 Simplifying w = 3.476476035Subproblem 2
w + -0.3 = -3.176476035 Simplifying w + -0.3 = -3.176476035 Reorder the terms: -0.3 + w = -3.176476035 Solving -0.3 + w = -3.176476035 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + w = -3.176476035 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + w = -3.176476035 + 0.3 w = -3.176476035 + 0.3 Combine like terms: -3.176476035 + 0.3 = -2.876476035 w = -2.876476035 Simplifying w = -2.876476035Solution
The solution to the problem is based on the solutions from the subproblems. w = {3.476476035, -2.876476035}
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