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Simplifying -12x4 + 21x2 + -2 = 0 Reorder the terms: -2 + 21x2 + -12x4 = 0 Solving -2 + 21x2 + -12x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. 0.1666666667 + -1.75x2 + x4 = 0 Move the constant term to the right: Add '-0.1666666667' to each side of the equation. 0.1666666667 + -1.75x2 + -0.1666666667 + x4 = 0 + -0.1666666667 Reorder the terms: 0.1666666667 + -0.1666666667 + -1.75x2 + x4 = 0 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + -1.75x2 + x4 = 0 + -0.1666666667 -1.75x2 + x4 = 0 + -0.1666666667 Combine like terms: 0 + -0.1666666667 = -0.1666666667 -1.75x2 + x4 = -0.1666666667 The x term is -1.75x2. Take half its coefficient (-0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. -1.75x2 + 0.765625 + x4 = -0.1666666667 + 0.765625 Reorder the terms: 0.765625 + -1.75x2 + x4 = -0.1666666667 + 0.765625 Combine like terms: -0.1666666667 + 0.765625 = 0.5989583333 0.765625 + -1.75x2 + x4 = 0.5989583333 Factor a perfect square on the left side: (x2 + -0.875)(x2 + -0.875) = 0.5989583333 Calculate the square root of the right side: 0.773923984 Break this problem into two subproblems by setting (x2 + -0.875) equal to 0.773923984 and -0.773923984.Subproblem 1
x2 + -0.875 = 0.773923984 Simplifying x2 + -0.875 = 0.773923984 Reorder the terms: -0.875 + x2 = 0.773923984 Solving -0.875 + x2 = 0.773923984 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x2 = 0.773923984 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x2 = 0.773923984 + 0.875 x2 = 0.773923984 + 0.875 Combine like terms: 0.773923984 + 0.875 = 1.648923984 x2 = 1.648923984 Simplifying x2 = 1.648923984 Take the square root of each side: x = {-1.284104351, 1.284104351}Subproblem 2
x2 + -0.875 = -0.773923984 Simplifying x2 + -0.875 = -0.773923984 Reorder the terms: -0.875 + x2 = -0.773923984 Solving -0.875 + x2 = -0.773923984 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x2 = -0.773923984 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x2 = -0.773923984 + 0.875 x2 = -0.773923984 + 0.875 Combine like terms: -0.773923984 + 0.875 = 0.101076016 x2 = 0.101076016 Simplifying x2 = 0.101076016 Take the square root of each side: x = {-0.317924545, 0.317924545}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.284104351, 1.284104351, -0.317924545, 0.317924545}
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