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Simplifying 9x2 + -36x + -1848 = 0 Reorder the terms: -1848 + -36x + 9x2 = 0 Solving -1848 + -36x + 9x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-616 + -12x + 3x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-616 + -12x + 3x2)' equal to zero and attempt to solve: Simplifying -616 + -12x + 3x2 = 0 Solving -616 + -12x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -205.3333333 + -4x + x2 = 0 Move the constant term to the right: Add '205.3333333' to each side of the equation. -205.3333333 + -4x + 205.3333333 + x2 = 0 + 205.3333333 Reorder the terms: -205.3333333 + 205.3333333 + -4x + x2 = 0 + 205.3333333 Combine like terms: -205.3333333 + 205.3333333 = 0.0000000 0.0000000 + -4x + x2 = 0 + 205.3333333 -4x + x2 = 0 + 205.3333333 Combine like terms: 0 + 205.3333333 = 205.3333333 -4x + x2 = 205.3333333 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 205.3333333 + 4 Reorder the terms: 4 + -4x + x2 = 205.3333333 + 4 Combine like terms: 205.3333333 + 4 = 209.3333333 4 + -4x + x2 = 209.3333333 Factor a perfect square on the left side: (x + -2)(x + -2) = 209.3333333 Calculate the square root of the right side: 14.468356275 Break this problem into two subproblems by setting (x + -2) equal to 14.468356275 and -14.468356275.Subproblem 1
x + -2 = 14.468356275 Simplifying x + -2 = 14.468356275 Reorder the terms: -2 + x = 14.468356275 Solving -2 + x = 14.468356275 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 + x = 14.468356275 + 2 Combine like terms: -2 + 2 = 0 0 + x = 14.468356275 + 2 x = 14.468356275 + 2 Combine like terms: 14.468356275 + 2 = 16.468356275 x = 16.468356275 Simplifying x = 16.468356275Subproblem 2
x + -2 = -14.468356275 Simplifying x + -2 = -14.468356275 Reorder the terms: -2 + x = -14.468356275 Solving -2 + x = -14.468356275 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 + x = -14.468356275 + 2 Combine like terms: -2 + 2 = 0 0 + x = -14.468356275 + 2 x = -14.468356275 + 2 Combine like terms: -14.468356275 + 2 = -12.468356275 x = -12.468356275 Simplifying x = -12.468356275Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.468356275, -12.468356275}Solution
x = {16.468356275, -12.468356275}
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