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Simplifying 7x[4x + -3(x + -1)] = x + 2 Reorder the terms: 7x[4x + -3(-1 + x)] = x + 2 7x[4x + (-1 * -3 + x * -3)] = x + 2 7x[4x + (3 + -3x)] = x + 2 Reorder the terms: 7x[3 + 4x + -3x] = x + 2 Combine like terms: 4x + -3x = 1x 7x[3 + 1x] = x + 2 [3 * 7x + 1x * 7x] = x + 2 [21x + 7x2] = x + 2 Reorder the terms: 21x + 7x2 = 2 + x Solving 21x + 7x2 = 2 + x Solving for variable 'x'. Reorder the terms: -2 + 21x + -1x + 7x2 = 2 + x + -2 + -1x Combine like terms: 21x + -1x = 20x -2 + 20x + 7x2 = 2 + x + -2 + -1x Reorder the terms: -2 + 20x + 7x2 = 2 + -2 + x + -1x Combine like terms: 2 + -2 = 0 -2 + 20x + 7x2 = 0 + x + -1x -2 + 20x + 7x2 = x + -1x Combine like terms: x + -1x = 0 -2 + 20x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.2857142857 + 2.857142857x + x2 = 0 Move the constant term to the right: Add '0.2857142857' to each side of the equation. -0.2857142857 + 2.857142857x + 0.2857142857 + x2 = 0 + 0.2857142857 Reorder the terms: -0.2857142857 + 0.2857142857 + 2.857142857x + x2 = 0 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + 2.857142857x + x2 = 0 + 0.2857142857 2.857142857x + x2 = 0 + 0.2857142857 Combine like terms: 0 + 0.2857142857 = 0.2857142857 2.857142857x + x2 = 0.2857142857 The x term is 2.857142857x. Take half its coefficient (1.428571429). Square it (2.040816328) and add it to both sides. Add '2.040816328' to each side of the equation. 2.857142857x + 2.040816328 + x2 = 0.2857142857 + 2.040816328 Reorder the terms: 2.040816328 + 2.857142857x + x2 = 0.2857142857 + 2.040816328 Combine like terms: 0.2857142857 + 2.040816328 = 2.3265306137 2.040816328 + 2.857142857x + x2 = 2.3265306137 Factor a perfect square on the left side: (x + 1.428571429)(x + 1.428571429) = 2.3265306137 Calculate the square root of the right side: 1.525296894 Break this problem into two subproblems by setting (x + 1.428571429) equal to 1.525296894 and -1.525296894.Subproblem 1
x + 1.428571429 = 1.525296894 Simplifying x + 1.428571429 = 1.525296894 Reorder the terms: 1.428571429 + x = 1.525296894 Solving 1.428571429 + x = 1.525296894 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.428571429' to each side of the equation. 1.428571429 + -1.428571429 + x = 1.525296894 + -1.428571429 Combine like terms: 1.428571429 + -1.428571429 = 0.000000000 0.000000000 + x = 1.525296894 + -1.428571429 x = 1.525296894 + -1.428571429 Combine like terms: 1.525296894 + -1.428571429 = 0.096725465 x = 0.096725465 Simplifying x = 0.096725465Subproblem 2
x + 1.428571429 = -1.525296894 Simplifying x + 1.428571429 = -1.525296894 Reorder the terms: 1.428571429 + x = -1.525296894 Solving 1.428571429 + x = -1.525296894 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.428571429' to each side of the equation. 1.428571429 + -1.428571429 + x = -1.525296894 + -1.428571429 Combine like terms: 1.428571429 + -1.428571429 = 0.000000000 0.000000000 + x = -1.525296894 + -1.428571429 x = -1.525296894 + -1.428571429 Combine like terms: -1.525296894 + -1.428571429 = -2.953868323 x = -2.953868323 Simplifying x = -2.953868323Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.096725465, -2.953868323}
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