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Simplifying (4w2 + -8w + -8) + -1(7w2 + 7w + -2) = 0 Reorder the terms: (-8 + -8w + 4w2) + -1(7w2 + 7w + -2) = 0 Remove parenthesis around (-8 + -8w + 4w2) -8 + -8w + 4w2 + -1(7w2 + 7w + -2) = 0 Reorder the terms: -8 + -8w + 4w2 + -1(-2 + 7w + 7w2) = 0 -8 + -8w + 4w2 + (-2 * -1 + 7w * -1 + 7w2 * -1) = 0 -8 + -8w + 4w2 + (2 + -7w + -7w2) = 0 Reorder the terms: -8 + 2 + -8w + -7w + 4w2 + -7w2 = 0 Combine like terms: -8 + 2 = -6 -6 + -8w + -7w + 4w2 + -7w2 = 0 Combine like terms: -8w + -7w = -15w -6 + -15w + 4w2 + -7w2 = 0 Combine like terms: 4w2 + -7w2 = -3w2 -6 + -15w + -3w2 = 0 Solving -6 + -15w + -3w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '-3'. -3(2 + 5w + w2) = 0 Ignore the factor -3.Subproblem 1
Set the factor '(2 + 5w + w2)' equal to zero and attempt to solve: Simplifying 2 + 5w + w2 = 0 Solving 2 + 5w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 5w + -2 + w2 = 0 + -2 Reorder the terms: 2 + -2 + 5w + w2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 5w + w2 = 0 + -2 5w + w2 = 0 + -2 Combine like terms: 0 + -2 = -2 5w + w2 = -2 The w term is 5w. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5w + 6.25 + w2 = -2 + 6.25 Reorder the terms: 6.25 + 5w + w2 = -2 + 6.25 Combine like terms: -2 + 6.25 = 4.25 6.25 + 5w + w2 = 4.25 Factor a perfect square on the left side: (w + 2.5)(w + 2.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (w + 2.5) equal to 2.061552813 and -2.061552813.Subproblem 1
w + 2.5 = 2.061552813 Simplifying w + 2.5 = 2.061552813 Reorder the terms: 2.5 + w = 2.061552813 Solving 2.5 + w = 2.061552813 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + w = 2.061552813 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + w = 2.061552813 + -2.5 w = 2.061552813 + -2.5 Combine like terms: 2.061552813 + -2.5 = -0.438447187 w = -0.438447187 Simplifying w = -0.438447187Subproblem 2
w + 2.5 = -2.061552813 Simplifying w + 2.5 = -2.061552813 Reorder the terms: 2.5 + w = -2.061552813 Solving 2.5 + w = -2.061552813 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + w = -2.061552813 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + w = -2.061552813 + -2.5 w = -2.061552813 + -2.5 Combine like terms: -2.061552813 + -2.5 = -4.561552813 w = -4.561552813 Simplifying w = -4.561552813Solution
The solution to the problem is based on the solutions from the subproblems. w = {-0.438447187, -4.561552813}Solution
w = {-0.438447187, -4.561552813}
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