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Simplifying 4w2 + 23w + -21 = 0 Reorder the terms: -21 + 23w + 4w2 = 0 Solving -21 + 23w + 4w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -5.25 + 5.75w + w2 = 0 Move the constant term to the right: Add '5.25' to each side of the equation. -5.25 + 5.75w + 5.25 + w2 = 0 + 5.25 Reorder the terms: -5.25 + 5.25 + 5.75w + w2 = 0 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + 5.75w + w2 = 0 + 5.25 5.75w + w2 = 0 + 5.25 Combine like terms: 0 + 5.25 = 5.25 5.75w + w2 = 5.25 The w term is 5.75w. Take half its coefficient (2.875). Square it (8.265625) and add it to both sides. Add '8.265625' to each side of the equation. 5.75w + 8.265625 + w2 = 5.25 + 8.265625 Reorder the terms: 8.265625 + 5.75w + w2 = 5.25 + 8.265625 Combine like terms: 5.25 + 8.265625 = 13.515625 8.265625 + 5.75w + w2 = 13.515625 Factor a perfect square on the left side: (w + 2.875)(w + 2.875) = 13.515625 Calculate the square root of the right side: 3.676360292 Break this problem into two subproblems by setting (w + 2.875) equal to 3.676360292 and -3.676360292.Subproblem 1
w + 2.875 = 3.676360292 Simplifying w + 2.875 = 3.676360292 Reorder the terms: 2.875 + w = 3.676360292 Solving 2.875 + w = 3.676360292 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2.875' to each side of the equation. 2.875 + -2.875 + w = 3.676360292 + -2.875 Combine like terms: 2.875 + -2.875 = 0.000 0.000 + w = 3.676360292 + -2.875 w = 3.676360292 + -2.875 Combine like terms: 3.676360292 + -2.875 = 0.801360292 w = 0.801360292 Simplifying w = 0.801360292Subproblem 2
w + 2.875 = -3.676360292 Simplifying w + 2.875 = -3.676360292 Reorder the terms: 2.875 + w = -3.676360292 Solving 2.875 + w = -3.676360292 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2.875' to each side of the equation. 2.875 + -2.875 + w = -3.676360292 + -2.875 Combine like terms: 2.875 + -2.875 = 0.000 0.000 + w = -3.676360292 + -2.875 w = -3.676360292 + -2.875 Combine like terms: -3.676360292 + -2.875 = -6.551360292 w = -6.551360292 Simplifying w = -6.551360292Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.801360292, -6.551360292}
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