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Simplifying -8x(3x + 4) + 6x = 4(x + -8) + 4x Reorder the terms: -8x(4 + 3x) + 6x = 4(x + -8) + 4x (4 * -8x + 3x * -8x) + 6x = 4(x + -8) + 4x (-32x + -24x2) + 6x = 4(x + -8) + 4x Reorder the terms: -32x + 6x + -24x2 = 4(x + -8) + 4x Combine like terms: -32x + 6x = -26x -26x + -24x2 = 4(x + -8) + 4x Reorder the terms: -26x + -24x2 = 4(-8 + x) + 4x -26x + -24x2 = (-8 * 4 + x * 4) + 4x -26x + -24x2 = (-32 + 4x) + 4x Combine like terms: 4x + 4x = 8x -26x + -24x2 = -32 + 8x Solving -26x + -24x2 = -32 + 8x Solving for variable 'x'. Reorder the terms: 32 + -26x + -8x + -24x2 = -32 + 8x + 32 + -8x Combine like terms: -26x + -8x = -34x 32 + -34x + -24x2 = -32 + 8x + 32 + -8x Reorder the terms: 32 + -34x + -24x2 = -32 + 32 + 8x + -8x Combine like terms: -32 + 32 = 0 32 + -34x + -24x2 = 0 + 8x + -8x 32 + -34x + -24x2 = 8x + -8x Combine like terms: 8x + -8x = 0 32 + -34x + -24x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(16 + -17x + -12x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(16 + -17x + -12x2)' equal to zero and attempt to solve: Simplifying 16 + -17x + -12x2 = 0 Solving 16 + -17x + -12x2 = 0 Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. -1.333333333 + 1.416666667x + x2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + 1.416666667x + 1.333333333 + x2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + 1.416666667x + x2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + 1.416666667x + x2 = 0 + 1.333333333 1.416666667x + x2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 1.416666667x + x2 = 1.333333333 The x term is 1.416666667x. Take half its coefficient (0.7083333335). Square it (0.5017361113) and add it to both sides. Add '0.5017361113' to each side of the equation. 1.416666667x + 0.5017361113 + x2 = 1.333333333 + 0.5017361113 Reorder the terms: 0.5017361113 + 1.416666667x + x2 = 1.333333333 + 0.5017361113 Combine like terms: 1.333333333 + 0.5017361113 = 1.8350694443 0.5017361113 + 1.416666667x + x2 = 1.8350694443 Factor a perfect square on the left side: (x + 0.7083333335)(x + 0.7083333335) = 1.8350694443 Calculate the square root of the right side: 1.354647351 Break this problem into two subproblems by setting (x + 0.7083333335) equal to 1.354647351 and -1.354647351.Subproblem 1
x + 0.7083333335 = 1.354647351 Simplifying x + 0.7083333335 = 1.354647351 Reorder the terms: 0.7083333335 + x = 1.354647351 Solving 0.7083333335 + x = 1.354647351 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7083333335' to each side of the equation. 0.7083333335 + -0.7083333335 + x = 1.354647351 + -0.7083333335 Combine like terms: 0.7083333335 + -0.7083333335 = 0.0000000000 0.0000000000 + x = 1.354647351 + -0.7083333335 x = 1.354647351 + -0.7083333335 Combine like terms: 1.354647351 + -0.7083333335 = 0.6463140175 x = 0.6463140175 Simplifying x = 0.6463140175Subproblem 2
x + 0.7083333335 = -1.354647351 Simplifying x + 0.7083333335 = -1.354647351 Reorder the terms: 0.7083333335 + x = -1.354647351 Solving 0.7083333335 + x = -1.354647351 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7083333335' to each side of the equation. 0.7083333335 + -0.7083333335 + x = -1.354647351 + -0.7083333335 Combine like terms: 0.7083333335 + -0.7083333335 = 0.0000000000 0.0000000000 + x = -1.354647351 + -0.7083333335 x = -1.354647351 + -0.7083333335 Combine like terms: -1.354647351 + -0.7083333335 = -2.0629806845 x = -2.0629806845 Simplifying x = -2.0629806845Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6463140175, -2.0629806845}Solution
x = {0.6463140175, -2.0629806845}
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