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Simplifying -4w2 + -14w + -9 = 0 Reorder the terms: -9 + -14w + -4w2 = 0 Solving -9 + -14w + -4w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '-1'. -1(9 + 14w + 4w2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(9 + 14w + 4w2)' equal to zero and attempt to solve: Simplifying 9 + 14w + 4w2 = 0 Solving 9 + 14w + 4w2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.25 + 3.5w + w2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + 3.5w + -2.25 + w2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + 3.5w + w2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + 3.5w + w2 = 0 + -2.25 3.5w + w2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 3.5w + w2 = -2.25 The w term is 3.5w. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5w + 3.0625 + w2 = -2.25 + 3.0625 Reorder the terms: 3.0625 + 3.5w + w2 = -2.25 + 3.0625 Combine like terms: -2.25 + 3.0625 = 0.8125 3.0625 + 3.5w + w2 = 0.8125 Factor a perfect square on the left side: (w + 1.75)(w + 1.75) = 0.8125 Calculate the square root of the right side: 0.901387819 Break this problem into two subproblems by setting (w + 1.75) equal to 0.901387819 and -0.901387819.Subproblem 1
w + 1.75 = 0.901387819 Simplifying w + 1.75 = 0.901387819 Reorder the terms: 1.75 + w = 0.901387819 Solving 1.75 + w = 0.901387819 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + w = 0.901387819 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + w = 0.901387819 + -1.75 w = 0.901387819 + -1.75 Combine like terms: 0.901387819 + -1.75 = -0.848612181 w = -0.848612181 Simplifying w = -0.848612181Subproblem 2
w + 1.75 = -0.901387819 Simplifying w + 1.75 = -0.901387819 Reorder the terms: 1.75 + w = -0.901387819 Solving 1.75 + w = -0.901387819 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + w = -0.901387819 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + w = -0.901387819 + -1.75 w = -0.901387819 + -1.75 Combine like terms: -0.901387819 + -1.75 = -2.651387819 w = -2.651387819 Simplifying w = -2.651387819Solution
The solution to the problem is based on the solutions from the subproblems. w = {-0.848612181, -2.651387819}Solution
w = {-0.848612181, -2.651387819}
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