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Simplifying w2 + 1510w + -32400 = 0 Reorder the terms: -32400 + 1510w + w2 = 0 Solving -32400 + 1510w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '32400' to each side of the equation. -32400 + 1510w + 32400 + w2 = 0 + 32400 Reorder the terms: -32400 + 32400 + 1510w + w2 = 0 + 32400 Combine like terms: -32400 + 32400 = 0 0 + 1510w + w2 = 0 + 32400 1510w + w2 = 0 + 32400 Combine like terms: 0 + 32400 = 32400 1510w + w2 = 32400 The w term is 1510w. Take half its coefficient (755). Square it (570025) and add it to both sides. Add '570025' to each side of the equation. 1510w + 570025 + w2 = 32400 + 570025 Reorder the terms: 570025 + 1510w + w2 = 32400 + 570025 Combine like terms: 32400 + 570025 = 602425 570025 + 1510w + w2 = 602425 Factor a perfect square on the left side: (w + 755)(w + 755) = 602425 Calculate the square root of the right side: 776.160421562 Break this problem into two subproblems by setting (w + 755) equal to 776.160421562 and -776.160421562.Subproblem 1
w + 755 = 776.160421562 Simplifying w + 755 = 776.160421562 Reorder the terms: 755 + w = 776.160421562 Solving 755 + w = 776.160421562 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-755' to each side of the equation. 755 + -755 + w = 776.160421562 + -755 Combine like terms: 755 + -755 = 0 0 + w = 776.160421562 + -755 w = 776.160421562 + -755 Combine like terms: 776.160421562 + -755 = 21.160421562 w = 21.160421562 Simplifying w = 21.160421562Subproblem 2
w + 755 = -776.160421562 Simplifying w + 755 = -776.160421562 Reorder the terms: 755 + w = -776.160421562 Solving 755 + w = -776.160421562 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-755' to each side of the equation. 755 + -755 + w = -776.160421562 + -755 Combine like terms: 755 + -755 = 0 0 + w = -776.160421562 + -755 w = -776.160421562 + -755 Combine like terms: -776.160421562 + -755 = -1531.160421562 w = -1531.160421562 Simplifying w = -1531.160421562Solution
The solution to the problem is based on the solutions from the subproblems. w = {21.160421562, -1531.160421562}
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