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Simplifying 5w2 + -23w + 10 = 0 Reorder the terms: 10 + -23w + 5w2 = 0 Solving 10 + -23w + 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 + -4.6w + w2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -4.6w + -2 + w2 = 0 + -2 Reorder the terms: 2 + -2 + -4.6w + w2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -4.6w + w2 = 0 + -2 -4.6w + w2 = 0 + -2 Combine like terms: 0 + -2 = -2 -4.6w + w2 = -2 The w term is -4.6w. Take half its coefficient (-2.3). Square it (5.29) and add it to both sides. Add '5.29' to each side of the equation. -4.6w + 5.29 + w2 = -2 + 5.29 Reorder the terms: 5.29 + -4.6w + w2 = -2 + 5.29 Combine like terms: -2 + 5.29 = 3.29 5.29 + -4.6w + w2 = 3.29 Factor a perfect square on the left side: (w + -2.3)(w + -2.3) = 3.29 Calculate the square root of the right side: 1.813835715 Break this problem into two subproblems by setting (w + -2.3) equal to 1.813835715 and -1.813835715.Subproblem 1
w + -2.3 = 1.813835715 Simplifying w + -2.3 = 1.813835715 Reorder the terms: -2.3 + w = 1.813835715 Solving -2.3 + w = 1.813835715 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2.3' to each side of the equation. -2.3 + 2.3 + w = 1.813835715 + 2.3 Combine like terms: -2.3 + 2.3 = 0.0 0.0 + w = 1.813835715 + 2.3 w = 1.813835715 + 2.3 Combine like terms: 1.813835715 + 2.3 = 4.113835715 w = 4.113835715 Simplifying w = 4.113835715Subproblem 2
w + -2.3 = -1.813835715 Simplifying w + -2.3 = -1.813835715 Reorder the terms: -2.3 + w = -1.813835715 Solving -2.3 + w = -1.813835715 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2.3' to each side of the equation. -2.3 + 2.3 + w = -1.813835715 + 2.3 Combine like terms: -2.3 + 2.3 = 0.0 0.0 + w = -1.813835715 + 2.3 w = -1.813835715 + 2.3 Combine like terms: -1.813835715 + 2.3 = 0.486164285 w = 0.486164285 Simplifying w = 0.486164285Solution
The solution to the problem is based on the solutions from the subproblems. w = {4.113835715, 0.486164285}
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