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Simplifying -15x4 + -18x2 + 1 = 0 Reorder the terms: 1 + -18x2 + -15x4 = 0 Solving 1 + -18x2 + -15x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -15 the coefficient of the squared term: Divide each side by '-15'. -0.06666666667 + 1.2x2 + x4 = 0 Move the constant term to the right: Add '0.06666666667' to each side of the equation. -0.06666666667 + 1.2x2 + 0.06666666667 + x4 = 0 + 0.06666666667 Reorder the terms: -0.06666666667 + 0.06666666667 + 1.2x2 + x4 = 0 + 0.06666666667 Combine like terms: -0.06666666667 + 0.06666666667 = 0.00000000000 0.00000000000 + 1.2x2 + x4 = 0 + 0.06666666667 1.2x2 + x4 = 0 + 0.06666666667 Combine like terms: 0 + 0.06666666667 = 0.06666666667 1.2x2 + x4 = 0.06666666667 The x term is 1.2x2. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2x2 + 0.36 + x4 = 0.06666666667 + 0.36 Reorder the terms: 0.36 + 1.2x2 + x4 = 0.06666666667 + 0.36 Combine like terms: 0.06666666667 + 0.36 = 0.42666666667 0.36 + 1.2x2 + x4 = 0.42666666667 Factor a perfect square on the left side: (x2 + 0.6)(x2 + 0.6) = 0.42666666667 Calculate the square root of the right side: 0.653197265 Break this problem into two subproblems by setting (x2 + 0.6) equal to 0.653197265 and -0.653197265.Subproblem 1
x2 + 0.6 = 0.653197265 Simplifying x2 + 0.6 = 0.653197265 Reorder the terms: 0.6 + x2 = 0.653197265 Solving 0.6 + x2 = 0.653197265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x2 = 0.653197265 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x2 = 0.653197265 + -0.6 x2 = 0.653197265 + -0.6 Combine like terms: 0.653197265 + -0.6 = 0.053197265 x2 = 0.053197265 Simplifying x2 = 0.053197265 Take the square root of each side: x = {-0.230645323, 0.230645323}Subproblem 2
x2 + 0.6 = -0.653197265 Simplifying x2 + 0.6 = -0.653197265 Reorder the terms: 0.6 + x2 = -0.653197265 Solving 0.6 + x2 = -0.653197265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x2 = -0.653197265 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x2 = -0.653197265 + -0.6 x2 = -0.653197265 + -0.6 Combine like terms: -0.653197265 + -0.6 = -1.253197265 x2 = -1.253197265 Simplifying x2 = -1.253197265 Reorder the terms: 1.253197265 + x2 = -1.253197265 + 1.253197265 Combine like terms: -1.253197265 + 1.253197265 = 0.000000000 1.253197265 + 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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