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Simplifying 6 + -2(4 + -1x) * 3x = 5x + -2 Reorder the terms for easier multiplication: 6 + -2 * 3x(4 + -1x) = 5x + -2 Multiply -2 * 3 6 + -6x(4 + -1x) = 5x + -2 6 + (4 * -6x + -1x * -6x) = 5x + -2 6 + (-24x + 6x2) = 5x + -2 Reorder the terms: 6 + -24x + 6x2 = -2 + 5x Solving 6 + -24x + 6x2 = -2 + 5x Solving for variable 'x'. Reorder the terms: 6 + 2 + -24x + -5x + 6x2 = -2 + 5x + 2 + -5x Combine like terms: 6 + 2 = 8 8 + -24x + -5x + 6x2 = -2 + 5x + 2 + -5x Combine like terms: -24x + -5x = -29x 8 + -29x + 6x2 = -2 + 5x + 2 + -5x Reorder the terms: 8 + -29x + 6x2 = -2 + 2 + 5x + -5x Combine like terms: -2 + 2 = 0 8 + -29x + 6x2 = 0 + 5x + -5x 8 + -29x + 6x2 = 5x + -5x Combine like terms: 5x + -5x = 0 8 + -29x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1.333333333 + -4.833333333x + x2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + -4.833333333x + -1.333333333 + x2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + -4.833333333x + x2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + -4.833333333x + x2 = 0 + -1.333333333 -4.833333333x + x2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 -4.833333333x + x2 = -1.333333333 The x term is -4.833333333x. Take half its coefficient (-2.416666667). Square it (5.840277779) and add it to both sides. Add '5.840277779' to each side of the equation. -4.833333333x + 5.840277779 + x2 = -1.333333333 + 5.840277779 Reorder the terms: 5.840277779 + -4.833333333x + x2 = -1.333333333 + 5.840277779 Combine like terms: -1.333333333 + 5.840277779 = 4.506944446 5.840277779 + -4.833333333x + x2 = 4.506944446 Factor a perfect square on the left side: (x + -2.416666667)(x + -2.416666667) = 4.506944446 Calculate the square root of the right side: 2.122956534 Break this problem into two subproblems by setting (x + -2.416666667) equal to 2.122956534 and -2.122956534.Subproblem 1
x + -2.416666667 = 2.122956534 Simplifying x + -2.416666667 = 2.122956534 Reorder the terms: -2.416666667 + x = 2.122956534 Solving -2.416666667 + x = 2.122956534 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.416666667' to each side of the equation. -2.416666667 + 2.416666667 + x = 2.122956534 + 2.416666667 Combine like terms: -2.416666667 + 2.416666667 = 0.000000000 0.000000000 + x = 2.122956534 + 2.416666667 x = 2.122956534 + 2.416666667 Combine like terms: 2.122956534 + 2.416666667 = 4.539623201 x = 4.539623201 Simplifying x = 4.539623201Subproblem 2
x + -2.416666667 = -2.122956534 Simplifying x + -2.416666667 = -2.122956534 Reorder the terms: -2.416666667 + x = -2.122956534 Solving -2.416666667 + x = -2.122956534 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.416666667' to each side of the equation. -2.416666667 + 2.416666667 + x = -2.122956534 + 2.416666667 Combine like terms: -2.416666667 + 2.416666667 = 0.000000000 0.000000000 + x = -2.122956534 + 2.416666667 x = -2.122956534 + 2.416666667 Combine like terms: -2.122956534 + 2.416666667 = 0.293710133 x = 0.293710133 Simplifying x = 0.293710133Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.539623201, 0.293710133}
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