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Simplifying -5w2 + 24w + 22 = 0 Reorder the terms: 22 + 24w + -5w2 = 0 Solving 22 + 24w + -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'. -4.4 + -4.8w + w2 = 0 Move the constant term to the right: Add '4.4' to each side of the equation. -4.4 + -4.8w + 4.4 + w2 = 0 + 4.4 Reorder the terms: -4.4 + 4.4 + -4.8w + w2 = 0 + 4.4 Combine like terms: -4.4 + 4.4 = 0.0 0.0 + -4.8w + w2 = 0 + 4.4 -4.8w + w2 = 0 + 4.4 Combine like terms: 0 + 4.4 = 4.4 -4.8w + w2 = 4.4 The w term is -4.8w. Take half its coefficient (-2.4). Square it (5.76) and add it to both sides. Add '5.76' to each side of the equation. -4.8w + 5.76 + w2 = 4.4 + 5.76 Reorder the terms: 5.76 + -4.8w + w2 = 4.4 + 5.76 Combine like terms: 4.4 + 5.76 = 10.16 5.76 + -4.8w + w2 = 10.16 Factor a perfect square on the left side: (w + -2.4)(w + -2.4) = 10.16 Calculate the square root of the right side: 3.18747549 Break this problem into two subproblems by setting (w + -2.4) equal to 3.18747549 and -3.18747549.Subproblem 1
w + -2.4 = 3.18747549 Simplifying w + -2.4 = 3.18747549 Reorder the terms: -2.4 + w = 3.18747549 Solving -2.4 + w = 3.18747549 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2.4' to each side of the equation. -2.4 + 2.4 + w = 3.18747549 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + w = 3.18747549 + 2.4 w = 3.18747549 + 2.4 Combine like terms: 3.18747549 + 2.4 = 5.58747549 w = 5.58747549 Simplifying w = 5.58747549Subproblem 2
w + -2.4 = -3.18747549 Simplifying w + -2.4 = -3.18747549 Reorder the terms: -2.4 + w = -3.18747549 Solving -2.4 + w = -3.18747549 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2.4' to each side of the equation. -2.4 + 2.4 + w = -3.18747549 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + w = -3.18747549 + 2.4 w = -3.18747549 + 2.4 Combine like terms: -3.18747549 + 2.4 = -0.78747549 w = -0.78747549 Simplifying w = -0.78747549Solution
The solution to the problem is based on the solutions from the subproblems. w = {5.58747549, -0.78747549}
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