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Simplifying -7(1 + -4x) = 3(x + -11) * 12x (1 * -7 + -4x * -7) = 3(x + -11) * 12x (-7 + 28x) = 3(x + -11) * 12x Reorder the terms: -7 + 28x = 3(-11 + x) * 12x Reorder the terms for easier multiplication: -7 + 28x = 3 * 12x(-11 + x) Multiply 3 * 12 -7 + 28x = 36x(-11 + x) -7 + 28x = (-11 * 36x + x * 36x) -7 + 28x = (-396x + 36x2) Solving -7 + 28x = -396x + 36x2 Solving for variable 'x'. Combine like terms: 28x + 396x = 424x -7 + 424x + -36x2 = -396x + 36x2 + 396x + -36x2 Reorder the terms: -7 + 424x + -36x2 = -396x + 396x + 36x2 + -36x2 Combine like terms: -396x + 396x = 0 -7 + 424x + -36x2 = 0 + 36x2 + -36x2 -7 + 424x + -36x2 = 36x2 + -36x2 Combine like terms: 36x2 + -36x2 = 0 -7 + 424x + -36x2 = 0 Begin completing the square. Divide all terms by -36 the coefficient of the squared term: Divide each side by '-36'. 0.1944444444 + -11.77777778x + x2 = 0 Move the constant term to the right: Add '-0.1944444444' to each side of the equation. 0.1944444444 + -11.77777778x + -0.1944444444 + x2 = 0 + -0.1944444444 Reorder the terms: 0.1944444444 + -0.1944444444 + -11.77777778x + x2 = 0 + -0.1944444444 Combine like terms: 0.1944444444 + -0.1944444444 = 0.0000000000 0.0000000000 + -11.77777778x + x2 = 0 + -0.1944444444 -11.77777778x + x2 = 0 + -0.1944444444 Combine like terms: 0 + -0.1944444444 = -0.1944444444 -11.77777778x + x2 = -0.1944444444 The x term is -11.77777778x. Take half its coefficient (-5.88888889). Square it (34.67901236) and add it to both sides. Add '34.67901236' to each side of the equation. -11.77777778x + 34.67901236 + x2 = -0.1944444444 + 34.67901236 Reorder the terms: 34.67901236 + -11.77777778x + x2 = -0.1944444444 + 34.67901236 Combine like terms: -0.1944444444 + 34.67901236 = 34.4845679156 34.67901236 + -11.77777778x + x2 = 34.4845679156 Factor a perfect square on the left side: (x + -5.88888889)(x + -5.88888889) = 34.4845679156 Calculate the square root of the right side: 5.872356249 Break this problem into two subproblems by setting (x + -5.88888889) equal to 5.872356249 and -5.872356249.Subproblem 1
x + -5.88888889 = 5.872356249 Simplifying x + -5.88888889 = 5.872356249 Reorder the terms: -5.88888889 + x = 5.872356249 Solving -5.88888889 + x = 5.872356249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.88888889' to each side of the equation. -5.88888889 + 5.88888889 + x = 5.872356249 + 5.88888889 Combine like terms: -5.88888889 + 5.88888889 = 0.00000000 0.00000000 + x = 5.872356249 + 5.88888889 x = 5.872356249 + 5.88888889 Combine like terms: 5.872356249 + 5.88888889 = 11.761245139 x = 11.761245139 Simplifying x = 11.761245139Subproblem 2
x + -5.88888889 = -5.872356249 Simplifying x + -5.88888889 = -5.872356249 Reorder the terms: -5.88888889 + x = -5.872356249 Solving -5.88888889 + x = -5.872356249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.88888889' to each side of the equation. -5.88888889 + 5.88888889 + x = -5.872356249 + 5.88888889 Combine like terms: -5.88888889 + 5.88888889 = 0.00000000 0.00000000 + x = -5.872356249 + 5.88888889 x = -5.872356249 + 5.88888889 Combine like terms: -5.872356249 + 5.88888889 = 0.016532641 x = 0.016532641 Simplifying x = 0.016532641Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.761245139, 0.016532641}
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