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Simplifying 5w2 + -11w + -10 = 0 Reorder the terms: -10 + -11w + 5w2 = 0 Solving -10 + -11w + 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'. -2 + -2.2w + w2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -2.2w + 2 + w2 = 0 + 2 Reorder the terms: -2 + 2 + -2.2w + w2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -2.2w + w2 = 0 + 2 -2.2w + w2 = 0 + 2 Combine like terms: 0 + 2 = 2 -2.2w + w2 = 2 The w term is -2.2w. Take half its coefficient (-1.1). Square it (1.21) and add it to both sides. Add '1.21' to each side of the equation. -2.2w + 1.21 + w2 = 2 + 1.21 Reorder the terms: 1.21 + -2.2w + w2 = 2 + 1.21 Combine like terms: 2 + 1.21 = 3.21 1.21 + -2.2w + w2 = 3.21 Factor a perfect square on the left side: (w + -1.1)(w + -1.1) = 3.21 Calculate the square root of the right side: 1.791647287 Break this problem into two subproblems by setting (w + -1.1) equal to 1.791647287 and -1.791647287.Subproblem 1
w + -1.1 = 1.791647287 Simplifying w + -1.1 = 1.791647287 Reorder the terms: -1.1 + w = 1.791647287 Solving -1.1 + w = 1.791647287 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + w = 1.791647287 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + w = 1.791647287 + 1.1 w = 1.791647287 + 1.1 Combine like terms: 1.791647287 + 1.1 = 2.891647287 w = 2.891647287 Simplifying w = 2.891647287Subproblem 2
w + -1.1 = -1.791647287 Simplifying w + -1.1 = -1.791647287 Reorder the terms: -1.1 + w = -1.791647287 Solving -1.1 + w = -1.791647287 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + w = -1.791647287 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + w = -1.791647287 + 1.1 w = -1.791647287 + 1.1 Combine like terms: -1.791647287 + 1.1 = -0.691647287 w = -0.691647287 Simplifying w = -0.691647287Solution
The solution to the problem is based on the solutions from the subproblems. w = {2.891647287, -0.691647287}
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