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Simplifying w2 + 2w + -70 = 0 Reorder the terms: -70 + 2w + w2 = 0 Solving -70 + 2w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '70' to each side of the equation. -70 + 2w + 70 + w2 = 0 + 70 Reorder the terms: -70 + 70 + 2w + w2 = 0 + 70 Combine like terms: -70 + 70 = 0 0 + 2w + w2 = 0 + 70 2w + w2 = 0 + 70 Combine like terms: 0 + 70 = 70 2w + w2 = 70 The w term is 2w. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2w + 1 + w2 = 70 + 1 Reorder the terms: 1 + 2w + w2 = 70 + 1 Combine like terms: 70 + 1 = 71 1 + 2w + w2 = 71 Factor a perfect square on the left side: (w + 1)(w + 1) = 71 Calculate the square root of the right side: 8.426149773 Break this problem into two subproblems by setting (w + 1) equal to 8.426149773 and -8.426149773.Subproblem 1
w + 1 = 8.426149773 Simplifying w + 1 = 8.426149773 Reorder the terms: 1 + w = 8.426149773 Solving 1 + w = 8.426149773 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + w = 8.426149773 + -1 Combine like terms: 1 + -1 = 0 0 + w = 8.426149773 + -1 w = 8.426149773 + -1 Combine like terms: 8.426149773 + -1 = 7.426149773 w = 7.426149773 Simplifying w = 7.426149773Subproblem 2
w + 1 = -8.426149773 Simplifying w + 1 = -8.426149773 Reorder the terms: 1 + w = -8.426149773 Solving 1 + w = -8.426149773 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + w = -8.426149773 + -1 Combine like terms: 1 + -1 = 0 0 + w = -8.426149773 + -1 w = -8.426149773 + -1 Combine like terms: -8.426149773 + -1 = -9.426149773 w = -9.426149773 Simplifying w = -9.426149773Solution
The solution to the problem is based on the solutions from the subproblems. w = {7.426149773, -9.426149773}
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