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Simplifying w(w + 4) = 70 Reorder the terms: w(4 + w) = 70 (4 * w + w * w) = 70 (4w + w2) = 70 Solving 4w + w2 = 70 Solving for variable 'w'. Reorder the terms: -70 + 4w + w2 = 70 + -70 Combine like terms: 70 + -70 = 0 -70 + 4w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '70' to each side of the equation. -70 + 4w + 70 + w2 = 0 + 70 Reorder the terms: -70 + 70 + 4w + w2 = 0 + 70 Combine like terms: -70 + 70 = 0 0 + 4w + w2 = 0 + 70 4w + w2 = 0 + 70 Combine like terms: 0 + 70 = 70 4w + w2 = 70 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 = 70 + 4 Reorder the terms: 4 + 4w + w2 = 70 + 4 Combine like terms: 70 + 4 = 74 4 + 4w + w2 = 74 Factor a perfect square on the left side: (w + 2)(w + 2) = 74 Calculate the square root of the right side: 8.602325267 Break this problem into two subproblems by setting (w + 2) equal to 8.602325267 and -8.602325267.Subproblem 1
w + 2 = 8.602325267 Simplifying w + 2 = 8.602325267 Reorder the terms: 2 + w = 8.602325267 Solving 2 + w = 8.602325267 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 = 8.602325267 + -2 Combine like terms: 2 + -2 = 0 0 + w = 8.602325267 + -2 w = 8.602325267 + -2 Combine like terms: 8.602325267 + -2 = 6.602325267 w = 6.602325267 Simplifying w = 6.602325267Subproblem 2
w + 2 = -8.602325267 Simplifying w + 2 = -8.602325267 Reorder the terms: 2 + w = -8.602325267 Solving 2 + w = -8.602325267 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 = -8.602325267 + -2 Combine like terms: 2 + -2 = 0 0 + w = -8.602325267 + -2 w = -8.602325267 + -2 Combine like terms: -8.602325267 + -2 = -10.602325267 w = -10.602325267 Simplifying w = -10.602325267Solution
The solution to the problem is based on the solutions from the subproblems. w = {6.602325267, -10.602325267}
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