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Simplifying 7x2 + -39x + 30 = 0 Reorder the terms: 30 + -39x + 7x2 = 0 Solving 30 + -39x + 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'. 4.285714286 + -5.571428571x + x2 = 0 Move the constant term to the right: Add '-4.285714286' to each side of the equation. 4.285714286 + -5.571428571x + -4.285714286 + x2 = 0 + -4.285714286 Reorder the terms: 4.285714286 + -4.285714286 + -5.571428571x + x2 = 0 + -4.285714286 Combine like terms: 4.285714286 + -4.285714286 = 0.000000000 0.000000000 + -5.571428571x + x2 = 0 + -4.285714286 -5.571428571x + x2 = 0 + -4.285714286 Combine like terms: 0 + -4.285714286 = -4.285714286 -5.571428571x + x2 = -4.285714286 The x term is -5.571428571x. Take half its coefficient (-2.785714286). Square it (7.760204083) and add it to both sides. Add '7.760204083' to each side of the equation. -5.571428571x + 7.760204083 + x2 = -4.285714286 + 7.760204083 Reorder the terms: 7.760204083 + -5.571428571x + x2 = -4.285714286 + 7.760204083 Combine like terms: -4.285714286 + 7.760204083 = 3.474489797 7.760204083 + -5.571428571x + x2 = 3.474489797 Factor a perfect square on the left side: (x + -2.785714286)(x + -2.785714286) = 3.474489797 Calculate the square root of the right side: 1.863998336 Break this problem into two subproblems by setting (x + -2.785714286) equal to 1.863998336 and -1.863998336.Subproblem 1
x + -2.785714286 = 1.863998336 Simplifying x + -2.785714286 = 1.863998336 Reorder the terms: -2.785714286 + x = 1.863998336 Solving -2.785714286 + x = 1.863998336 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.785714286' to each side of the equation. -2.785714286 + 2.785714286 + x = 1.863998336 + 2.785714286 Combine like terms: -2.785714286 + 2.785714286 = 0.000000000 0.000000000 + x = 1.863998336 + 2.785714286 x = 1.863998336 + 2.785714286 Combine like terms: 1.863998336 + 2.785714286 = 4.649712622 x = 4.649712622 Simplifying x = 4.649712622Subproblem 2
x + -2.785714286 = -1.863998336 Simplifying x + -2.785714286 = -1.863998336 Reorder the terms: -2.785714286 + x = -1.863998336 Solving -2.785714286 + x = -1.863998336 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.785714286' to each side of the equation. -2.785714286 + 2.785714286 + x = -1.863998336 + 2.785714286 Combine like terms: -2.785714286 + 2.785714286 = 0.000000000 0.000000000 + x = -1.863998336 + 2.785714286 x = -1.863998336 + 2.785714286 Combine like terms: -1.863998336 + 2.785714286 = 0.92171595 x = 0.92171595 Simplifying x = 0.92171595Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.649712622, 0.92171595}
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