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Simplifying 8x(3x + 6) = 4 + -1x Reorder the terms: 8x(6 + 3x) = 4 + -1x (6 * 8x + 3x * 8x) = 4 + -1x (48x + 24x2) = 4 + -1x Solving 48x + 24x2 = 4 + -1x Solving for variable 'x'. Reorder the terms: -4 + 48x + x + 24x2 = 4 + -1x + -4 + x Combine like terms: 48x + x = 49x -4 + 49x + 24x2 = 4 + -1x + -4 + x Reorder the terms: -4 + 49x + 24x2 = 4 + -4 + -1x + x Combine like terms: 4 + -4 = 0 -4 + 49x + 24x2 = 0 + -1x + x -4 + 49x + 24x2 = -1x + x Combine like terms: -1x + x = 0 -4 + 49x + 24x2 = 0 Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. -0.1666666667 + 2.041666667x + x2 = 0 Move the constant term to the right: Add '0.1666666667' to each side of the equation. -0.1666666667 + 2.041666667x + 0.1666666667 + x2 = 0 + 0.1666666667 Reorder the terms: -0.1666666667 + 0.1666666667 + 2.041666667x + x2 = 0 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + 2.041666667x + x2 = 0 + 0.1666666667 2.041666667x + x2 = 0 + 0.1666666667 Combine like terms: 0 + 0.1666666667 = 0.1666666667 2.041666667x + x2 = 0.1666666667 The x term is 2.041666667x. Take half its coefficient (1.020833334). Square it (1.042100696) and add it to both sides. Add '1.042100696' to each side of the equation. 2.041666667x + 1.042100696 + x2 = 0.1666666667 + 1.042100696 Reorder the terms: 1.042100696 + 2.041666667x + x2 = 0.1666666667 + 1.042100696 Combine like terms: 0.1666666667 + 1.042100696 = 1.2087673627 1.042100696 + 2.041666667x + x2 = 1.2087673627 Factor a perfect square on the left side: (x + 1.020833334)(x + 1.020833334) = 1.2087673627 Calculate the square root of the right side: 1.099439568 Break this problem into two subproblems by setting (x + 1.020833334) equal to 1.099439568 and -1.099439568.Subproblem 1
x + 1.020833334 = 1.099439568 Simplifying x + 1.020833334 = 1.099439568 Reorder the terms: 1.020833334 + x = 1.099439568 Solving 1.020833334 + x = 1.099439568 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.020833334' to each side of the equation. 1.020833334 + -1.020833334 + x = 1.099439568 + -1.020833334 Combine like terms: 1.020833334 + -1.020833334 = 0.000000000 0.000000000 + x = 1.099439568 + -1.020833334 x = 1.099439568 + -1.020833334 Combine like terms: 1.099439568 + -1.020833334 = 0.078606234 x = 0.078606234 Simplifying x = 0.078606234Subproblem 2
x + 1.020833334 = -1.099439568 Simplifying x + 1.020833334 = -1.099439568 Reorder the terms: 1.020833334 + x = -1.099439568 Solving 1.020833334 + x = -1.099439568 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.020833334' to each side of the equation. 1.020833334 + -1.020833334 + x = -1.099439568 + -1.020833334 Combine like terms: 1.020833334 + -1.020833334 = 0.000000000 0.000000000 + x = -1.099439568 + -1.020833334 x = -1.099439568 + -1.020833334 Combine like terms: -1.099439568 + -1.020833334 = -2.120272902 x = -2.120272902 Simplifying x = -2.120272902Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.078606234, -2.120272902}
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