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Simplifying 12x(7x + -4) = 44 Reorder the terms: 12x(-4 + 7x) = 44 (-4 * 12x + 7x * 12x) = 44 (-48x + 84x2) = 44 Solving -48x + 84x2 = 44 Solving for variable 'x'. Reorder the terms: -44 + -48x + 84x2 = 44 + -44 Combine like terms: 44 + -44 = 0 -44 + -48x + 84x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-11 + -12x + 21x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-11 + -12x + 21x2)' equal to zero and attempt to solve: Simplifying -11 + -12x + 21x2 = 0 Solving -11 + -12x + 21x2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -0.5238095238 + -0.5714285714x + x2 = 0 Move the constant term to the right: Add '0.5238095238' to each side of the equation. -0.5238095238 + -0.5714285714x + 0.5238095238 + x2 = 0 + 0.5238095238 Reorder the terms: -0.5238095238 + 0.5238095238 + -0.5714285714x + x2 = 0 + 0.5238095238 Combine like terms: -0.5238095238 + 0.5238095238 = 0.0000000000 0.0000000000 + -0.5714285714x + x2 = 0 + 0.5238095238 -0.5714285714x + x2 = 0 + 0.5238095238 Combine like terms: 0 + 0.5238095238 = 0.5238095238 -0.5714285714x + x2 = 0.5238095238 The x term is -0.5714285714x. Take half its coefficient (-0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. -0.5714285714x + 0.08163265305 + x2 = 0.5238095238 + 0.08163265305 Reorder the terms: 0.08163265305 + -0.5714285714x + x2 = 0.5238095238 + 0.08163265305 Combine like terms: 0.5238095238 + 0.08163265305 = 0.60544217685 0.08163265305 + -0.5714285714x + x2 = 0.60544217685 Factor a perfect square on the left side: (x + -0.2857142857)(x + -0.2857142857) = 0.60544217685 Calculate the square root of the right side: 0.778101649 Break this problem into two subproblems by setting (x + -0.2857142857) equal to 0.778101649 and -0.778101649.Subproblem 1
x + -0.2857142857 = 0.778101649 Simplifying x + -0.2857142857 = 0.778101649 Reorder the terms: -0.2857142857 + x = 0.778101649 Solving -0.2857142857 + x = 0.778101649 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + x = 0.778101649 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = 0.778101649 + 0.2857142857 x = 0.778101649 + 0.2857142857 Combine like terms: 0.778101649 + 0.2857142857 = 1.0638159347 x = 1.0638159347 Simplifying x = 1.0638159347Subproblem 2
x + -0.2857142857 = -0.778101649 Simplifying x + -0.2857142857 = -0.778101649 Reorder the terms: -0.2857142857 + x = -0.778101649 Solving -0.2857142857 + x = -0.778101649 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + x = -0.778101649 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = -0.778101649 + 0.2857142857 x = -0.778101649 + 0.2857142857 Combine like terms: -0.778101649 + 0.2857142857 = -0.4923873633 x = -0.4923873633 Simplifying x = -0.4923873633Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0638159347, -0.4923873633}Solution
x = {1.0638159347, -0.4923873633}
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