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Simplifying -8x6 + -24x5 + 22x4 = 0 Reorder the terms: 22x4 + -24x5 + -8x6 = 0 Solving 22x4 + -24x5 + -8x6 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x4'. 2x4(11 + -12x + -4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'x4' equal to zero and attempt to solve: Simplifying x4 = 0 Solving x4 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x4 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(11 + -12x + -4x2)' equal to zero and attempt to solve: Simplifying 11 + -12x + -4x2 = 0 Solving 11 + -12x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -2.75 + 3x + x2 = 0 Move the constant term to the right: Add '2.75' to each side of the equation. -2.75 + 3x + 2.75 + x2 = 0 + 2.75 Reorder the terms: -2.75 + 2.75 + 3x + x2 = 0 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + 3x + x2 = 0 + 2.75 3x + x2 = 0 + 2.75 Combine like terms: 0 + 2.75 = 2.75 3x + x2 = 2.75 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 2.75 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 2.75 + 2.25 Combine like terms: 2.75 + 2.25 = 5 2.25 + 3x + x2 = 5 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (x + 1.5) equal to 2.236067978 and -2.236067978.Subproblem 1
x + 1.5 = 2.236067978 Simplifying x + 1.5 = 2.236067978 Reorder the terms: 1.5 + x = 2.236067978 Solving 1.5 + x = 2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 2.236067978 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 2.236067978 + -1.5 x = 2.236067978 + -1.5 Combine like terms: 2.236067978 + -1.5 = 0.736067978 x = 0.736067978 Simplifying x = 0.736067978Subproblem 2
x + 1.5 = -2.236067978 Simplifying x + 1.5 = -2.236067978 Reorder the terms: 1.5 + x = -2.236067978 Solving 1.5 + x = -2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -2.236067978 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -2.236067978 + -1.5 x = -2.236067978 + -1.5 Combine like terms: -2.236067978 + -1.5 = -3.736067978 x = -3.736067978 Simplifying x = -3.736067978Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.736067978, -3.736067978}Solution
x = {0.736067978, -3.736067978}
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