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Simplifying 3w2 + 4w + -13 = 2 + -2w Reorder the terms: -13 + 4w + 3w2 = 2 + -2w Solving -13 + 4w + 3w2 = 2 + -2w Solving for variable 'w'. Reorder the terms: -13 + -2 + 4w + 2w + 3w2 = 2 + -2w + -2 + 2w Combine like terms: -13 + -2 = -15 -15 + 4w + 2w + 3w2 = 2 + -2w + -2 + 2w Combine like terms: 4w + 2w = 6w -15 + 6w + 3w2 = 2 + -2w + -2 + 2w Reorder the terms: -15 + 6w + 3w2 = 2 + -2 + -2w + 2w Combine like terms: 2 + -2 = 0 -15 + 6w + 3w2 = 0 + -2w + 2w -15 + 6w + 3w2 = -2w + 2w Combine like terms: -2w + 2w = 0 -15 + 6w + 3w2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-5 + 2w + w2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + 2w + w2)' equal to zero and attempt to solve: Simplifying -5 + 2w + w2 = 0 Solving -5 + 2w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + 2w + 5 + w2 = 0 + 5 Reorder the terms: -5 + 5 + 2w + w2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 2w + w2 = 0 + 5 2w + w2 = 0 + 5 Combine like terms: 0 + 5 = 5 2w + w2 = 5 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 = 5 + 1 Reorder the terms: 1 + 2w + w2 = 5 + 1 Combine like terms: 5 + 1 = 6 1 + 2w + w2 = 6 Factor a perfect square on the left side: (w + 1)(w + 1) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (w + 1) equal to 2.449489743 and -2.449489743.Subproblem 1
w + 1 = 2.449489743 Simplifying w + 1 = 2.449489743 Reorder the terms: 1 + w = 2.449489743 Solving 1 + w = 2.449489743 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 = 2.449489743 + -1 Combine like terms: 1 + -1 = 0 0 + w = 2.449489743 + -1 w = 2.449489743 + -1 Combine like terms: 2.449489743 + -1 = 1.449489743 w = 1.449489743 Simplifying w = 1.449489743Subproblem 2
w + 1 = -2.449489743 Simplifying w + 1 = -2.449489743 Reorder the terms: 1 + w = -2.449489743 Solving 1 + w = -2.449489743 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 = -2.449489743 + -1 Combine like terms: 1 + -1 = 0 0 + w = -2.449489743 + -1 w = -2.449489743 + -1 Combine like terms: -2.449489743 + -1 = -3.449489743 w = -3.449489743 Simplifying w = -3.449489743Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.449489743, -3.449489743}Solution
w = {1.449489743, -3.449489743}
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