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Simplifying 3x4 + 5x2 = 13 Reorder the terms: 5x2 + 3x4 = 13 Solving 5x2 + 3x4 = 13 Solving for variable 'x'. Reorder the terms: -13 + 5x2 + 3x4 = 13 + -13 Combine like terms: 13 + -13 = 0 -13 + 5x2 + 3x4 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -4.333333333 + 1.666666667x2 + x4 = 0 Move the constant term to the right: Add '4.333333333' to each side of the equation. -4.333333333 + 1.666666667x2 + 4.333333333 + x4 = 0 + 4.333333333 Reorder the terms: -4.333333333 + 4.333333333 + 1.666666667x2 + x4 = 0 + 4.333333333 Combine like terms: -4.333333333 + 4.333333333 = 0.000000000 0.000000000 + 1.666666667x2 + x4 = 0 + 4.333333333 1.666666667x2 + x4 = 0 + 4.333333333 Combine like terms: 0 + 4.333333333 = 4.333333333 1.666666667x2 + x4 = 4.333333333 The x term is 1.666666667x2. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667x2 + 0.6944444447 + x4 = 4.333333333 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x2 + x4 = 4.333333333 + 0.6944444447 Combine like terms: 4.333333333 + 0.6944444447 = 5.0277777777 0.6944444447 + 1.666666667x2 + x4 = 5.0277777777 Factor a perfect square on the left side: (x2 + 0.8333333335)(x2 + 0.8333333335) = 5.0277777777 Calculate the square root of the right side: 2.242270674 Break this problem into two subproblems by setting (x2 + 0.8333333335) equal to 2.242270674 and -2.242270674.Subproblem 1
x2 + 0.8333333335 = 2.242270674 Simplifying x2 + 0.8333333335 = 2.242270674 Reorder the terms: 0.8333333335 + x2 = 2.242270674 Solving 0.8333333335 + x2 = 2.242270674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x2 = 2.242270674 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x2 = 2.242270674 + -0.8333333335 x2 = 2.242270674 + -0.8333333335 Combine like terms: 2.242270674 + -0.8333333335 = 1.4089373405 x2 = 1.4089373405 Simplifying x2 = 1.4089373405 Take the square root of each side: x = {-1.186986664, 1.186986664}Subproblem 2
x2 + 0.8333333335 = -2.242270674 Simplifying x2 + 0.8333333335 = -2.242270674 Reorder the terms: 0.8333333335 + x2 = -2.242270674 Solving 0.8333333335 + x2 = -2.242270674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x2 = -2.242270674 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x2 = -2.242270674 + -0.8333333335 x2 = -2.242270674 + -0.8333333335 Combine like terms: -2.242270674 + -0.8333333335 = -3.0756040075 x2 = -3.0756040075 Simplifying x2 = -3.0756040075 Reorder the terms: 3.0756040075 + x2 = -3.0756040075 + 3.0756040075 Combine like terms: -3.0756040075 + 3.0756040075 = 0.0000000000 3.0756040075 + 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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