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Simplifying 7x(x + -6) + 6x = 10 Reorder the terms: 7x(-6 + x) + 6x = 10 (-6 * 7x + x * 7x) + 6x = 10 (-42x + 7x2) + 6x = 10 Reorder the terms: -42x + 6x + 7x2 = 10 Combine like terms: -42x + 6x = -36x -36x + 7x2 = 10 Solving -36x + 7x2 = 10 Solving for variable 'x'. Reorder the terms: -10 + -36x + 7x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + -36x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.428571429 + -5.142857143x + x2 = 0 Move the constant term to the right: Add '1.428571429' to each side of the equation. -1.428571429 + -5.142857143x + 1.428571429 + x2 = 0 + 1.428571429 Reorder the terms: -1.428571429 + 1.428571429 + -5.142857143x + x2 = 0 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + -5.142857143x + x2 = 0 + 1.428571429 -5.142857143x + x2 = 0 + 1.428571429 Combine like terms: 0 + 1.428571429 = 1.428571429 -5.142857143x + x2 = 1.428571429 The x term is -5.142857143x. Take half its coefficient (-2.571428572). Square it (6.612244901) and add it to both sides. Add '6.612244901' to each side of the equation. -5.142857143x + 6.612244901 + x2 = 1.428571429 + 6.612244901 Reorder the terms: 6.612244901 + -5.142857143x + x2 = 1.428571429 + 6.612244901 Combine like terms: 1.428571429 + 6.612244901 = 8.04081633 6.612244901 + -5.142857143x + x2 = 8.04081633 Factor a perfect square on the left side: (x + -2.571428572)(x + -2.571428572) = 8.04081633 Calculate the square root of the right side: 2.835633321 Break this problem into two subproblems by setting (x + -2.571428572) equal to 2.835633321 and -2.835633321.Subproblem 1
x + -2.571428572 = 2.835633321 Simplifying x + -2.571428572 = 2.835633321 Reorder the terms: -2.571428572 + x = 2.835633321 Solving -2.571428572 + x = 2.835633321 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.571428572' to each side of the equation. -2.571428572 + 2.571428572 + x = 2.835633321 + 2.571428572 Combine like terms: -2.571428572 + 2.571428572 = 0.000000000 0.000000000 + x = 2.835633321 + 2.571428572 x = 2.835633321 + 2.571428572 Combine like terms: 2.835633321 + 2.571428572 = 5.407061893 x = 5.407061893 Simplifying x = 5.407061893Subproblem 2
x + -2.571428572 = -2.835633321 Simplifying x + -2.571428572 = -2.835633321 Reorder the terms: -2.571428572 + x = -2.835633321 Solving -2.571428572 + x = -2.835633321 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.571428572' to each side of the equation. -2.571428572 + 2.571428572 + x = -2.835633321 + 2.571428572 Combine like terms: -2.571428572 + 2.571428572 = 0.000000000 0.000000000 + x = -2.835633321 + 2.571428572 x = -2.835633321 + 2.571428572 Combine like terms: -2.835633321 + 2.571428572 = -0.264204749 x = -0.264204749 Simplifying x = -0.264204749Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.407061893, -0.264204749}
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