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Simplifying 7x2 + -36x + 27 = 0 Reorder the terms: 27 + -36x + 7x2 = 0 Solving 27 + -36x + 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'. 3.857142857 + -5.142857143x + x2 = 0 Move the constant term to the right: Add '-3.857142857' to each side of the equation. 3.857142857 + -5.142857143x + -3.857142857 + x2 = 0 + -3.857142857 Reorder the terms: 3.857142857 + -3.857142857 + -5.142857143x + x2 = 0 + -3.857142857 Combine like terms: 3.857142857 + -3.857142857 = 0.000000000 0.000000000 + -5.142857143x + x2 = 0 + -3.857142857 -5.142857143x + x2 = 0 + -3.857142857 Combine like terms: 0 + -3.857142857 = -3.857142857 -5.142857143x + x2 = -3.857142857 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 = -3.857142857 + 6.612244901 Reorder the terms: 6.612244901 + -5.142857143x + x2 = -3.857142857 + 6.612244901 Combine like terms: -3.857142857 + 6.612244901 = 2.755102044 6.612244901 + -5.142857143x + x2 = 2.755102044 Factor a perfect square on the left side: (x + -2.571428572)(x + -2.571428572) = 2.755102044 Calculate the square root of the right side: 1.659850006 Break this problem into two subproblems by setting (x + -2.571428572) equal to 1.659850006 and -1.659850006.Subproblem 1
x + -2.571428572 = 1.659850006 Simplifying x + -2.571428572 = 1.659850006 Reorder the terms: -2.571428572 + x = 1.659850006 Solving -2.571428572 + x = 1.659850006 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 = 1.659850006 + 2.571428572 Combine like terms: -2.571428572 + 2.571428572 = 0.000000000 0.000000000 + x = 1.659850006 + 2.571428572 x = 1.659850006 + 2.571428572 Combine like terms: 1.659850006 + 2.571428572 = 4.231278578 x = 4.231278578 Simplifying x = 4.231278578Subproblem 2
x + -2.571428572 = -1.659850006 Simplifying x + -2.571428572 = -1.659850006 Reorder the terms: -2.571428572 + x = -1.659850006 Solving -2.571428572 + x = -1.659850006 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 = -1.659850006 + 2.571428572 Combine like terms: -2.571428572 + 2.571428572 = 0.000000000 0.000000000 + x = -1.659850006 + 2.571428572 x = -1.659850006 + 2.571428572 Combine like terms: -1.659850006 + 2.571428572 = 0.911578566 x = 0.911578566 Simplifying x = 0.911578566Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.231278578, 0.911578566}
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