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Simplifying 6x2 + -8x + -18 = 6 Reorder the terms: -18 + -8x + 6x2 = 6 Solving -18 + -8x + 6x2 = 6 Solving for variable 'x'. Reorder the terms: -18 + -6 + -8x + 6x2 = 6 + -6 Combine like terms: -18 + -6 = -24 -24 + -8x + 6x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -24 + -8x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + -4x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-12 + -4x + 3x2)' equal to zero and attempt to solve: Simplifying -12 + -4x + 3x2 = 0 Solving -12 + -4x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -4 + -1.333333333x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -1.333333333x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -1.333333333x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1.333333333x + x2 = 0 + 4 -1.333333333x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -1.333333333x + x2 = 4 The x term is -1.333333333x. Take half its coefficient (-0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. -1.333333333x + 0.4444444442 + x2 = 4 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = 4 + 0.4444444442 Combine like terms: 4 + 0.4444444442 = 4.4444444442 0.4444444442 + -1.333333333x + x2 = 4.4444444442 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = 4.4444444442 Calculate the square root of the right side: 2.108185107 Break this problem into two subproblems by setting (x + -0.6666666665) equal to 2.108185107 and -2.108185107.Subproblem 1
x + -0.6666666665 = 2.108185107 Simplifying x + -0.6666666665 = 2.108185107 Reorder the terms: -0.6666666665 + x = 2.108185107 Solving -0.6666666665 + x = 2.108185107 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = 2.108185107 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = 2.108185107 + 0.6666666665 x = 2.108185107 + 0.6666666665 Combine like terms: 2.108185107 + 0.6666666665 = 2.7748517735 x = 2.7748517735 Simplifying x = 2.7748517735Subproblem 2
x + -0.6666666665 = -2.108185107 Simplifying x + -0.6666666665 = -2.108185107 Reorder the terms: -0.6666666665 + x = -2.108185107 Solving -0.6666666665 + x = -2.108185107 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = -2.108185107 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = -2.108185107 + 0.6666666665 x = -2.108185107 + 0.6666666665 Combine like terms: -2.108185107 + 0.6666666665 = -1.4415184405 x = -1.4415184405 Simplifying x = -1.4415184405Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.7748517735, -1.4415184405}Solution
x = {2.7748517735, -1.4415184405}
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