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Simplifying 5x4 + 18x2 + 7 = 0 Reorder the terms: 7 + 18x2 + 5x4 = 0 Solving 7 + 18x2 + 5x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.4 + 3.6x2 + x4 = 0 Move the constant term to the right: Add '-1.4' to each side of the equation. 1.4 + 3.6x2 + -1.4 + x4 = 0 + -1.4 Reorder the terms: 1.4 + -1.4 + 3.6x2 + x4 = 0 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + 3.6x2 + x4 = 0 + -1.4 3.6x2 + x4 = 0 + -1.4 Combine like terms: 0 + -1.4 = -1.4 3.6x2 + x4 = -1.4 The x term is 3.6x2. Take half its coefficient (1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. 3.6x2 + 3.24 + x4 = -1.4 + 3.24 Reorder the terms: 3.24 + 3.6x2 + x4 = -1.4 + 3.24 Combine like terms: -1.4 + 3.24 = 1.84 3.24 + 3.6x2 + x4 = 1.84 Factor a perfect square on the left side: (x2 + 1.8)(x2 + 1.8) = 1.84 Calculate the square root of the right side: 1.356465997 Break this problem into two subproblems by setting (x2 + 1.8) equal to 1.356465997 and -1.356465997.Subproblem 1
x2 + 1.8 = 1.356465997 Simplifying x2 + 1.8 = 1.356465997 Reorder the terms: 1.8 + x2 = 1.356465997 Solving 1.8 + x2 = 1.356465997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + x2 = 1.356465997 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + x2 = 1.356465997 + -1.8 x2 = 1.356465997 + -1.8 Combine like terms: 1.356465997 + -1.8 = -0.443534003 x2 = -0.443534003 Simplifying x2 = -0.443534003 Reorder the terms: 0.443534003 + x2 = -0.443534003 + 0.443534003 Combine like terms: -0.443534003 + 0.443534003 = 0.000000000 0.443534003 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x2 + 1.8 = -1.356465997 Simplifying x2 + 1.8 = -1.356465997 Reorder the terms: 1.8 + x2 = -1.356465997 Solving 1.8 + x2 = -1.356465997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + x2 = -1.356465997 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + x2 = -1.356465997 + -1.8 x2 = -1.356465997 + -1.8 Combine like terms: -1.356465997 + -1.8 = -3.156465997 x2 = -3.156465997 Simplifying x2 = -3.156465997 Reorder the terms: 3.156465997 + x2 = -3.156465997 + 3.156465997 Combine like terms: -3.156465997 + 3.156465997 = 0.000000000 3.156465997 + x2 = 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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