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Simplifying 5x4 + 3x2 = 1 Reorder the terms: 3x2 + 5x4 = 1 Solving 3x2 + 5x4 = 1 Solving for variable 'x'. Reorder the terms: -1 + 3x2 + 5x4 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + 3x2 + 5x4 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.2 + 0.6x2 + x4 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + 0.6x2 + 0.2 + x4 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + 0.6x2 + x4 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + 0.6x2 + x4 = 0 + 0.2 0.6x2 + x4 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 0.6x2 + x4 = 0.2 The x term is 0.6x2. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6x2 + 0.09 + x4 = 0.2 + 0.09 Reorder the terms: 0.09 + 0.6x2 + x4 = 0.2 + 0.09 Combine like terms: 0.2 + 0.09 = 0.29 0.09 + 0.6x2 + x4 = 0.29 Factor a perfect square on the left side: (x2 + 0.3)(x2 + 0.3) = 0.29 Calculate the square root of the right side: 0.538516481 Break this problem into two subproblems by setting (x2 + 0.3) equal to 0.538516481 and -0.538516481.Subproblem 1
x2 + 0.3 = 0.538516481 Simplifying x2 + 0.3 = 0.538516481 Reorder the terms: 0.3 + x2 = 0.538516481 Solving 0.3 + x2 = 0.538516481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x2 = 0.538516481 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x2 = 0.538516481 + -0.3 x2 = 0.538516481 + -0.3 Combine like terms: 0.538516481 + -0.3 = 0.238516481 x2 = 0.238516481 Simplifying x2 = 0.238516481 Take the square root of each side: x = {-0.488381491, 0.488381491}Subproblem 2
x2 + 0.3 = -0.538516481 Simplifying x2 + 0.3 = -0.538516481 Reorder the terms: 0.3 + x2 = -0.538516481 Solving 0.3 + x2 = -0.538516481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x2 = -0.538516481 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x2 = -0.538516481 + -0.3 x2 = -0.538516481 + -0.3 Combine like terms: -0.538516481 + -0.3 = -0.838516481 x2 = -0.838516481 Simplifying x2 = -0.838516481 Reorder the terms: 0.838516481 + x2 = -0.838516481 + 0.838516481 Combine like terms: -0.838516481 + 0.838516481 = 0.000000000 0.838516481 + 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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