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Simplifying w4 + -1w2 + -10 = 0 Reorder the terms: -10 + -1w2 + w4 = 0 Solving -10 + -1w2 + w4 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + -1w2 + 10 + w4 = 0 + 10 Reorder the terms: -10 + 10 + -1w2 + w4 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -1w2 + w4 = 0 + 10 -1w2 + w4 = 0 + 10 Combine like terms: 0 + 10 = 10 -1w2 + w4 = 10 The w term is -1w2. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1w2 + 0.25 + w4 = 10 + 0.25 Reorder the terms: 0.25 + -1w2 + w4 = 10 + 0.25 Combine like terms: 10 + 0.25 = 10.25 0.25 + -1w2 + w4 = 10.25 Factor a perfect square on the left side: (w2 + -0.5)(w2 + -0.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (w2 + -0.5) equal to 3.201562119 and -3.201562119.Subproblem 1
w2 + -0.5 = 3.201562119 Simplifying w2 + -0.5 = 3.201562119 Reorder the terms: -0.5 + w2 = 3.201562119 Solving -0.5 + w2 = 3.201562119 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + w2 = 3.201562119 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + w2 = 3.201562119 + 0.5 w2 = 3.201562119 + 0.5 Combine like terms: 3.201562119 + 0.5 = 3.701562119 w2 = 3.701562119 Simplifying w2 = 3.701562119 Take the square root of each side: w = {-1.923944417, 1.923944417}Subproblem 2
w2 + -0.5 = -3.201562119 Simplifying w2 + -0.5 = -3.201562119 Reorder the terms: -0.5 + w2 = -3.201562119 Solving -0.5 + w2 = -3.201562119 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + w2 = -3.201562119 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + w2 = -3.201562119 + 0.5 w2 = -3.201562119 + 0.5 Combine like terms: -3.201562119 + 0.5 = -2.701562119 w2 = -2.701562119 Simplifying w2 = -2.701562119 Reorder the terms: 2.701562119 + w2 = -2.701562119 + 2.701562119 Combine like terms: -2.701562119 + 2.701562119 = 0.000000000 2.701562119 + w2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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