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Simplifying 24x2 + -162x + -324 = 0 Reorder the terms: -324 + -162x + 24x2 = 0 Solving -324 + -162x + 24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(-54 + -27x + 4x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-54 + -27x + 4x2)' equal to zero and attempt to solve: Simplifying -54 + -27x + 4x2 = 0 Solving -54 + -27x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -13.5 + -6.75x + x2 = 0 Move the constant term to the right: Add '13.5' to each side of the equation. -13.5 + -6.75x + 13.5 + x2 = 0 + 13.5 Reorder the terms: -13.5 + 13.5 + -6.75x + x2 = 0 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + -6.75x + x2 = 0 + 13.5 -6.75x + x2 = 0 + 13.5 Combine like terms: 0 + 13.5 = 13.5 -6.75x + x2 = 13.5 The x term is -6.75x. Take half its coefficient (-3.375). Square it (11.390625) and add it to both sides. Add '11.390625' to each side of the equation. -6.75x + 11.390625 + x2 = 13.5 + 11.390625 Reorder the terms: 11.390625 + -6.75x + x2 = 13.5 + 11.390625 Combine like terms: 13.5 + 11.390625 = 24.890625 11.390625 + -6.75x + x2 = 24.890625 Factor a perfect square on the left side: (x + -3.375)(x + -3.375) = 24.890625 Calculate the square root of the right side: 4.989050511 Break this problem into two subproblems by setting (x + -3.375) equal to 4.989050511 and -4.989050511.Subproblem 1
x + -3.375 = 4.989050511 Simplifying x + -3.375 = 4.989050511 Reorder the terms: -3.375 + x = 4.989050511 Solving -3.375 + x = 4.989050511 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.375' to each side of the equation. -3.375 + 3.375 + x = 4.989050511 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + x = 4.989050511 + 3.375 x = 4.989050511 + 3.375 Combine like terms: 4.989050511 + 3.375 = 8.364050511 x = 8.364050511 Simplifying x = 8.364050511Subproblem 2
x + -3.375 = -4.989050511 Simplifying x + -3.375 = -4.989050511 Reorder the terms: -3.375 + x = -4.989050511 Solving -3.375 + x = -4.989050511 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.375' to each side of the equation. -3.375 + 3.375 + x = -4.989050511 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + x = -4.989050511 + 3.375 x = -4.989050511 + 3.375 Combine like terms: -4.989050511 + 3.375 = -1.614050511 x = -1.614050511 Simplifying x = -1.614050511Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.364050511, -1.614050511}Solution
x = {8.364050511, -1.614050511}
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