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Simplifying w(w + -4) = 144 Reorder the terms: w(-4 + w) = 144 (-4 * w + w * w) = 144 (-4w + w2) = 144 Solving -4w + w2 = 144 Solving for variable 'w'. Reorder the terms: -144 + -4w + w2 = 144 + -144 Combine like terms: 144 + -144 = 0 -144 + -4w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '144' to each side of the equation. -144 + -4w + 144 + w2 = 0 + 144 Reorder the terms: -144 + 144 + -4w + w2 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + -4w + w2 = 0 + 144 -4w + w2 = 0 + 144 Combine like terms: 0 + 144 = 144 -4w + w2 = 144 The w term is -4w. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4w + 4 + w2 = 144 + 4 Reorder the terms: 4 + -4w + w2 = 144 + 4 Combine like terms: 144 + 4 = 148 4 + -4w + w2 = 148 Factor a perfect square on the left side: (w + -2)(w + -2) = 148 Calculate the square root of the right side: 12.165525061 Break this problem into two subproblems by setting (w + -2) equal to 12.165525061 and -12.165525061.Subproblem 1
w + -2 = 12.165525061 Simplifying w + -2 = 12.165525061 Reorder the terms: -2 + w = 12.165525061 Solving -2 + w = 12.165525061 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + w = 12.165525061 + 2 Combine like terms: -2 + 2 = 0 0 + w = 12.165525061 + 2 w = 12.165525061 + 2 Combine like terms: 12.165525061 + 2 = 14.165525061 w = 14.165525061 Simplifying w = 14.165525061Subproblem 2
w + -2 = -12.165525061 Simplifying w + -2 = -12.165525061 Reorder the terms: -2 + w = -12.165525061 Solving -2 + w = -12.165525061 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + w = -12.165525061 + 2 Combine like terms: -2 + 2 = 0 0 + w = -12.165525061 + 2 w = -12.165525061 + 2 Combine like terms: -12.165525061 + 2 = -10.165525061 w = -10.165525061 Simplifying w = -10.165525061Solution
The solution to the problem is based on the solutions from the subproblems. w = {14.165525061, -10.165525061}
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