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Simplifying 34x4 + 29x2 + -7 = 0 Reorder the terms: -7 + 29x2 + 34x4 = 0 Solving -7 + 29x2 + 34x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 34 the coefficient of the squared term: Divide each side by '34'. -0.2058823529 + 0.8529411765x2 + x4 = 0 Move the constant term to the right: Add '0.2058823529' to each side of the equation. -0.2058823529 + 0.8529411765x2 + 0.2058823529 + x4 = 0 + 0.2058823529 Reorder the terms: -0.2058823529 + 0.2058823529 + 0.8529411765x2 + x4 = 0 + 0.2058823529 Combine like terms: -0.2058823529 + 0.2058823529 = 0.0000000000 0.0000000000 + 0.8529411765x2 + x4 = 0 + 0.2058823529 0.8529411765x2 + x4 = 0 + 0.2058823529 Combine like terms: 0 + 0.2058823529 = 0.2058823529 0.8529411765x2 + x4 = 0.2058823529 The x term is 0.8529411765x2. Take half its coefficient (0.4264705883). Square it (0.1818771627) and add it to both sides. Add '0.1818771627' to each side of the equation. 0.8529411765x2 + 0.1818771627 + x4 = 0.2058823529 + 0.1818771627 Reorder the terms: 0.1818771627 + 0.8529411765x2 + x4 = 0.2058823529 + 0.1818771627 Combine like terms: 0.2058823529 + 0.1818771627 = 0.3877595156 0.1818771627 + 0.8529411765x2 + x4 = 0.3877595156 Factor a perfect square on the left side: (x2 + 0.4264705883)(x2 + 0.4264705883) = 0.3877595156 Calculate the square root of the right side: 0.622703393 Break this problem into two subproblems by setting (x2 + 0.4264705883) equal to 0.622703393 and -0.622703393.Subproblem 1
x2 + 0.4264705883 = 0.622703393 Simplifying x2 + 0.4264705883 = 0.622703393 Reorder the terms: 0.4264705883 + x2 = 0.622703393 Solving 0.4264705883 + x2 = 0.622703393 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4264705883' to each side of the equation. 0.4264705883 + -0.4264705883 + x2 = 0.622703393 + -0.4264705883 Combine like terms: 0.4264705883 + -0.4264705883 = 0.0000000000 0.0000000000 + x2 = 0.622703393 + -0.4264705883 x2 = 0.622703393 + -0.4264705883 Combine like terms: 0.622703393 + -0.4264705883 = 0.1962328047 x2 = 0.1962328047 Simplifying x2 = 0.1962328047 Take the square root of each side: x = {-0.442981721, 0.442981721}Subproblem 2
x2 + 0.4264705883 = -0.622703393 Simplifying x2 + 0.4264705883 = -0.622703393 Reorder the terms: 0.4264705883 + x2 = -0.622703393 Solving 0.4264705883 + x2 = -0.622703393 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4264705883' to each side of the equation. 0.4264705883 + -0.4264705883 + x2 = -0.622703393 + -0.4264705883 Combine like terms: 0.4264705883 + -0.4264705883 = 0.0000000000 0.0000000000 + x2 = -0.622703393 + -0.4264705883 x2 = -0.622703393 + -0.4264705883 Combine like terms: -0.622703393 + -0.4264705883 = -1.0491739813 x2 = -1.0491739813 Simplifying x2 = -1.0491739813 Reorder the terms: 1.0491739813 + x2 = -1.0491739813 + 1.0491739813 Combine like terms: -1.0491739813 + 1.0491739813 = 0.0000000000 1.0491739813 + 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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