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Simplifying -1w2 + -14w + 3 = 0 Reorder the terms: 3 + -14w + -1w2 = 0 Solving 3 + -14w + -1w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -3 + 14w + w2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 14w + 3 + w2 = 0 + 3 Reorder the terms: -3 + 3 + 14w + w2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 14w + w2 = 0 + 3 14w + w2 = 0 + 3 Combine like terms: 0 + 3 = 3 14w + w2 = 3 The w term is 14w. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14w + 49 + w2 = 3 + 49 Reorder the terms: 49 + 14w + w2 = 3 + 49 Combine like terms: 3 + 49 = 52 49 + 14w + w2 = 52 Factor a perfect square on the left side: (w + 7)(w + 7) = 52 Calculate the square root of the right side: 7.211102551 Break this problem into two subproblems by setting (w + 7) equal to 7.211102551 and -7.211102551.Subproblem 1
w + 7 = 7.211102551 Simplifying w + 7 = 7.211102551 Reorder the terms: 7 + w = 7.211102551 Solving 7 + w = 7.211102551 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + w = 7.211102551 + -7 Combine like terms: 7 + -7 = 0 0 + w = 7.211102551 + -7 w = 7.211102551 + -7 Combine like terms: 7.211102551 + -7 = 0.211102551 w = 0.211102551 Simplifying w = 0.211102551Subproblem 2
w + 7 = -7.211102551 Simplifying w + 7 = -7.211102551 Reorder the terms: 7 + w = -7.211102551 Solving 7 + w = -7.211102551 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + w = -7.211102551 + -7 Combine like terms: 7 + -7 = 0 0 + w = -7.211102551 + -7 w = -7.211102551 + -7 Combine like terms: -7.211102551 + -7 = -14.211102551 w = -14.211102551 Simplifying w = -14.211102551Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.211102551, -14.211102551}
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