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Simplifying 6x2 + -36x + -84 = 0 Reorder the terms: -84 + -36x + 6x2 = 0 Solving -84 + -36x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(-14 + -6x + x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-14 + -6x + x2)' equal to zero and attempt to solve: Simplifying -14 + -6x + x2 = 0 Solving -14 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + -6x + 14 + x2 = 0 + 14 Reorder the terms: -14 + 14 + -6x + x2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -6x + x2 = 0 + 14 -6x + x2 = 0 + 14 Combine like terms: 0 + 14 = 14 -6x + x2 = 14 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 14 + 9 Reorder the terms: 9 + -6x + x2 = 14 + 9 Combine like terms: 14 + 9 = 23 9 + -6x + x2 = 23 Factor a perfect square on the left side: (x + -3)(x + -3) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (x + -3) equal to 4.795831523 and -4.795831523.Subproblem 1
x + -3 = 4.795831523 Simplifying x + -3 = 4.795831523 Reorder the terms: -3 + x = 4.795831523 Solving -3 + x = 4.795831523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 4.795831523 + 3 Combine like terms: -3 + 3 = 0 0 + x = 4.795831523 + 3 x = 4.795831523 + 3 Combine like terms: 4.795831523 + 3 = 7.795831523 x = 7.795831523 Simplifying x = 7.795831523Subproblem 2
x + -3 = -4.795831523 Simplifying x + -3 = -4.795831523 Reorder the terms: -3 + x = -4.795831523 Solving -3 + x = -4.795831523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -4.795831523 + 3 Combine like terms: -3 + 3 = 0 0 + x = -4.795831523 + 3 x = -4.795831523 + 3 Combine like terms: -4.795831523 + 3 = -1.795831523 x = -1.795831523 Simplifying x = -1.795831523Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.795831523, -1.795831523}Solution
x = {7.795831523, -1.795831523}
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