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Simplifying -6x(x + 4) + -1x2 + 8 + -5x = 0 Reorder the terms: -6x(4 + x) + -1x2 + 8 + -5x = 0 (4 * -6x + x * -6x) + -1x2 + 8 + -5x = 0 (-24x + -6x2) + -1x2 + 8 + -5x = 0 Reorder the terms: 8 + -24x + -5x + -6x2 + -1x2 = 0 Combine like terms: -24x + -5x = -29x 8 + -29x + -6x2 + -1x2 = 0 Combine like terms: -6x2 + -1x2 = -7x2 8 + -29x + -7x2 = 0 Solving 8 + -29x + -7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -1.142857143 + 4.142857143x + x2 = 0 Move the constant term to the right: Add '1.142857143' to each side of the equation. -1.142857143 + 4.142857143x + 1.142857143 + x2 = 0 + 1.142857143 Reorder the terms: -1.142857143 + 1.142857143 + 4.142857143x + x2 = 0 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + 4.142857143x + x2 = 0 + 1.142857143 4.142857143x + x2 = 0 + 1.142857143 Combine like terms: 0 + 1.142857143 = 1.142857143 4.142857143x + x2 = 1.142857143 The x term is 4.142857143x. Take half its coefficient (2.071428572). Square it (4.290816329) and add it to both sides. Add '4.290816329' to each side of the equation. 4.142857143x + 4.290816329 + x2 = 1.142857143 + 4.290816329 Reorder the terms: 4.290816329 + 4.142857143x + x2 = 1.142857143 + 4.290816329 Combine like terms: 1.142857143 + 4.290816329 = 5.433673472 4.290816329 + 4.142857143x + x2 = 5.433673472 Factor a perfect square on the left side: (x + 2.071428572)(x + 2.071428572) = 5.433673472 Calculate the square root of the right side: 2.331024125 Break this problem into two subproblems by setting (x + 2.071428572) equal to 2.331024125 and -2.331024125.Subproblem 1
x + 2.071428572 = 2.331024125 Simplifying x + 2.071428572 = 2.331024125 Reorder the terms: 2.071428572 + x = 2.331024125 Solving 2.071428572 + x = 2.331024125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.071428572' to each side of the equation. 2.071428572 + -2.071428572 + x = 2.331024125 + -2.071428572 Combine like terms: 2.071428572 + -2.071428572 = 0.000000000 0.000000000 + x = 2.331024125 + -2.071428572 x = 2.331024125 + -2.071428572 Combine like terms: 2.331024125 + -2.071428572 = 0.259595553 x = 0.259595553 Simplifying x = 0.259595553Subproblem 2
x + 2.071428572 = -2.331024125 Simplifying x + 2.071428572 = -2.331024125 Reorder the terms: 2.071428572 + x = -2.331024125 Solving 2.071428572 + x = -2.331024125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.071428572' to each side of the equation. 2.071428572 + -2.071428572 + x = -2.331024125 + -2.071428572 Combine like terms: 2.071428572 + -2.071428572 = 0.000000000 0.000000000 + x = -2.331024125 + -2.071428572 x = -2.331024125 + -2.071428572 Combine like terms: -2.331024125 + -2.071428572 = -4.402452697 x = -4.402452697 Simplifying x = -4.402452697Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.259595553, -4.402452697}
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