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Simplifying 3x4 + -5x2 + 1.5 = 0 Reorder the terms: 1.5 + -5x2 + 3x4 = 0 Solving 1.5 + -5x2 + 3x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.5 + -1.666666667x2 + x4 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -1.666666667x2 + -0.5 + x4 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -1.666666667x2 + x4 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -1.666666667x2 + x4 = 0 + -0.5 -1.666666667x2 + x4 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -1.666666667x2 + x4 = -0.5 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 = -0.5 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x2 + x4 = -0.5 + 0.6944444447 Combine like terms: -0.5 + 0.6944444447 = 0.1944444447 0.6944444447 + -1.666666667x2 + x4 = 0.1944444447 Factor a perfect square on the left side: (x2 + -0.8333333335)(x2 + -0.8333333335) = 0.1944444447 Calculate the square root of the right side: 0.440958552 Break this problem into two subproblems by setting (x2 + -0.8333333335) equal to 0.440958552 and -0.440958552.Subproblem 1
x2 + -0.8333333335 = 0.440958552 Simplifying x2 + -0.8333333335 = 0.440958552 Reorder the terms: -0.8333333335 + x2 = 0.440958552 Solving -0.8333333335 + x2 = 0.440958552 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 = 0.440958552 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x2 = 0.440958552 + 0.8333333335 x2 = 0.440958552 + 0.8333333335 Combine like terms: 0.440958552 + 0.8333333335 = 1.2742918855 x2 = 1.2742918855 Simplifying x2 = 1.2742918855 Take the square root of each side: x = {-1.128845377, 1.128845377}Subproblem 2
x2 + -0.8333333335 = -0.440958552 Simplifying x2 + -0.8333333335 = -0.440958552 Reorder the terms: -0.8333333335 + x2 = -0.440958552 Solving -0.8333333335 + x2 = -0.440958552 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 = -0.440958552 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x2 = -0.440958552 + 0.8333333335 x2 = -0.440958552 + 0.8333333335 Combine like terms: -0.440958552 + 0.8333333335 = 0.3923747815 x2 = 0.3923747815 Simplifying x2 = 0.3923747815 Take the square root of each side: x = {-0.626398261, 0.626398261}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.128845377, 1.128845377, -0.626398261, 0.626398261}
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