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Simplifying 2x4 + -6x2 + 1 = 0 Reorder the terms: 1 + -6x2 + 2x4 = 0 Solving 1 + -6x2 + 2x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 0.5 + -3x2 + x4 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -3x2 + -0.5 + x4 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -3x2 + x4 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -3x2 + x4 = 0 + -0.5 -3x2 + x4 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -3x2 + x4 = -0.5 The x term is -3x2. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x2 + 2.25 + x4 = -0.5 + 2.25 Reorder the terms: 2.25 + -3x2 + x4 = -0.5 + 2.25 Combine like terms: -0.5 + 2.25 = 1.75 2.25 + -3x2 + x4 = 1.75 Factor a perfect square on the left side: (x2 + -1.5)(x2 + -1.5) = 1.75 Calculate the square root of the right side: 1.322875656 Break this problem into two subproblems by setting (x2 + -1.5) equal to 1.322875656 and -1.322875656.Subproblem 1
x2 + -1.5 = 1.322875656 Simplifying x2 + -1.5 = 1.322875656 Reorder the terms: -1.5 + x2 = 1.322875656 Solving -1.5 + x2 = 1.322875656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x2 = 1.322875656 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x2 = 1.322875656 + 1.5 x2 = 1.322875656 + 1.5 Combine like terms: 1.322875656 + 1.5 = 2.822875656 x2 = 2.822875656 Simplifying x2 = 2.822875656 Take the square root of each side: x = {-1.680141558, 1.680141558}Subproblem 2
x2 + -1.5 = -1.322875656 Simplifying x2 + -1.5 = -1.322875656 Reorder the terms: -1.5 + x2 = -1.322875656 Solving -1.5 + x2 = -1.322875656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x2 = -1.322875656 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x2 = -1.322875656 + 1.5 x2 = -1.322875656 + 1.5 Combine like terms: -1.322875656 + 1.5 = 0.177124344 x2 = 0.177124344 Simplifying x2 = 0.177124344 Take the square root of each side: x = {-0.420861431, 0.420861431}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.680141558, 1.680141558, -0.420861431, 0.420861431}
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