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Simplifying 3 + -3x4 + 12x2 = 0 Reorder the terms: 3 + 12x2 + -3x4 = 0 Solving 3 + 12x2 + -3x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(1 + 4x2 + -1x4) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1 + 4x2 + -1x4)' equal to zero and attempt to solve: Simplifying 1 + 4x2 + -1x4 = 0 Solving 1 + 4x2 + -1x4 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1 + -4x2 + x4 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -4x2 + 1 + x4 = 0 + 1 Reorder the terms: -1 + 1 + -4x2 + x4 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4x2 + x4 = 0 + 1 -4x2 + x4 = 0 + 1 Combine like terms: 0 + 1 = 1 -4x2 + x4 = 1 The x term is -4x2. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x2 + 4 + x4 = 1 + 4 Reorder the terms: 4 + -4x2 + x4 = 1 + 4 Combine like terms: 1 + 4 = 5 4 + -4x2 + x4 = 5 Factor a perfect square on the left side: (x2 + -2)(x2 + -2) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (x2 + -2) equal to 2.236067978 and -2.236067978.Subproblem 1
x2 + -2 = 2.236067978 Simplifying x2 + -2 = 2.236067978 Reorder the terms: -2 + x2 = 2.236067978 Solving -2 + x2 = 2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x2 = 2.236067978 + 2 Combine like terms: -2 + 2 = 0 0 + x2 = 2.236067978 + 2 x2 = 2.236067978 + 2 Combine like terms: 2.236067978 + 2 = 4.236067978 x2 = 4.236067978 Simplifying x2 = 4.236067978 Take the square root of each side: x = {-2.058171027, 2.058171027}Subproblem 2
x2 + -2 = -2.236067978 Simplifying x2 + -2 = -2.236067978 Reorder the terms: -2 + x2 = -2.236067978 Solving -2 + x2 = -2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x2 = -2.236067978 + 2 Combine like terms: -2 + 2 = 0 0 + x2 = -2.236067978 + 2 x2 = -2.236067978 + 2 Combine like terms: -2.236067978 + 2 = -0.236067978 x2 = -0.236067978 Simplifying x2 = -0.236067978 Reorder the terms: 0.236067978 + x2 = -0.236067978 + 0.236067978 Combine like terms: -0.236067978 + 0.236067978 = 0.000000000 0.236067978 + 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. 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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