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Simplifying 17x4 + 26x2 + -3 = 0 Reorder the terms: -3 + 26x2 + 17x4 = 0 Solving -3 + 26x2 + 17x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. -0.1764705882 + 1.529411765x2 + x4 = 0 Move the constant term to the right: Add '0.1764705882' to each side of the equation. -0.1764705882 + 1.529411765x2 + 0.1764705882 + x4 = 0 + 0.1764705882 Reorder the terms: -0.1764705882 + 0.1764705882 + 1.529411765x2 + x4 = 0 + 0.1764705882 Combine like terms: -0.1764705882 + 0.1764705882 = 0.0000000000 0.0000000000 + 1.529411765x2 + x4 = 0 + 0.1764705882 1.529411765x2 + x4 = 0 + 0.1764705882 Combine like terms: 0 + 0.1764705882 = 0.1764705882 1.529411765x2 + x4 = 0.1764705882 The x term is 1.529411765x2. Take half its coefficient (0.7647058825). Square it (0.5847750867) and add it to both sides. Add '0.5847750867' to each side of the equation. 1.529411765x2 + 0.5847750867 + x4 = 0.1764705882 + 0.5847750867 Reorder the terms: 0.5847750867 + 1.529411765x2 + x4 = 0.1764705882 + 0.5847750867 Combine like terms: 0.1764705882 + 0.5847750867 = 0.7612456749 0.5847750867 + 1.529411765x2 + x4 = 0.7612456749 Factor a perfect square on the left side: (x2 + 0.7647058825)(x2 + 0.7647058825) = 0.7612456749 Calculate the square root of the right side: 0.87249394 Break this problem into two subproblems by setting (x2 + 0.7647058825) equal to 0.87249394 and -0.87249394.Subproblem 1
x2 + 0.7647058825 = 0.87249394 Simplifying x2 + 0.7647058825 = 0.87249394 Reorder the terms: 0.7647058825 + x2 = 0.87249394 Solving 0.7647058825 + x2 = 0.87249394 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7647058825' to each side of the equation. 0.7647058825 + -0.7647058825 + x2 = 0.87249394 + -0.7647058825 Combine like terms: 0.7647058825 + -0.7647058825 = 0.0000000000 0.0000000000 + x2 = 0.87249394 + -0.7647058825 x2 = 0.87249394 + -0.7647058825 Combine like terms: 0.87249394 + -0.7647058825 = 0.1077880575 x2 = 0.1077880575 Simplifying x2 = 0.1077880575 Take the square root of each side: x = {-0.328310916, 0.328310916}Subproblem 2
x2 + 0.7647058825 = -0.87249394 Simplifying x2 + 0.7647058825 = -0.87249394 Reorder the terms: 0.7647058825 + x2 = -0.87249394 Solving 0.7647058825 + x2 = -0.87249394 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7647058825' to each side of the equation. 0.7647058825 + -0.7647058825 + x2 = -0.87249394 + -0.7647058825 Combine like terms: 0.7647058825 + -0.7647058825 = 0.0000000000 0.0000000000 + x2 = -0.87249394 + -0.7647058825 x2 = -0.87249394 + -0.7647058825 Combine like terms: -0.87249394 + -0.7647058825 = -1.6371998225 x2 = -1.6371998225 Simplifying x2 = -1.6371998225 Reorder the terms: 1.6371998225 + x2 = -1.6371998225 + 1.6371998225 Combine like terms: -1.6371998225 + 1.6371998225 = 0.0000000000 1.6371998225 + x2 = 0.0000000000 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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