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Simplifying 7x2 + -18x + -71 = 0 Reorder the terms: -71 + -18x + 7x2 = 0 Solving -71 + -18x + 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'. -10.14285714 + -2.571428571x + x2 = 0 Move the constant term to the right: Add '10.14285714' to each side of the equation. -10.14285714 + -2.571428571x + 10.14285714 + x2 = 0 + 10.14285714 Reorder the terms: -10.14285714 + 10.14285714 + -2.571428571x + x2 = 0 + 10.14285714 Combine like terms: -10.14285714 + 10.14285714 = 0.00000000 0.00000000 + -2.571428571x + x2 = 0 + 10.14285714 -2.571428571x + x2 = 0 + 10.14285714 Combine like terms: 0 + 10.14285714 = 10.14285714 -2.571428571x + x2 = 10.14285714 The x term is -2.571428571x. Take half its coefficient (-1.285714286). Square it (1.653061225) and add it to both sides. Add '1.653061225' to each side of the equation. -2.571428571x + 1.653061225 + x2 = 10.14285714 + 1.653061225 Reorder the terms: 1.653061225 + -2.571428571x + x2 = 10.14285714 + 1.653061225 Combine like terms: 10.14285714 + 1.653061225 = 11.795918365 1.653061225 + -2.571428571x + x2 = 11.795918365 Factor a perfect square on the left side: (x + -1.285714286)(x + -1.285714286) = 11.795918365 Calculate the square root of the right side: 3.434518651 Break this problem into two subproblems by setting (x + -1.285714286) equal to 3.434518651 and -3.434518651.Subproblem 1
x + -1.285714286 = 3.434518651 Simplifying x + -1.285714286 = 3.434518651 Reorder the terms: -1.285714286 + x = 3.434518651 Solving -1.285714286 + x = 3.434518651 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.285714286' to each side of the equation. -1.285714286 + 1.285714286 + x = 3.434518651 + 1.285714286 Combine like terms: -1.285714286 + 1.285714286 = 0.000000000 0.000000000 + x = 3.434518651 + 1.285714286 x = 3.434518651 + 1.285714286 Combine like terms: 3.434518651 + 1.285714286 = 4.720232937 x = 4.720232937 Simplifying x = 4.720232937Subproblem 2
x + -1.285714286 = -3.434518651 Simplifying x + -1.285714286 = -3.434518651 Reorder the terms: -1.285714286 + x = -3.434518651 Solving -1.285714286 + x = -3.434518651 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.285714286' to each side of the equation. -1.285714286 + 1.285714286 + x = -3.434518651 + 1.285714286 Combine like terms: -1.285714286 + 1.285714286 = 0.000000000 0.000000000 + x = -3.434518651 + 1.285714286 x = -3.434518651 + 1.285714286 Combine like terms: -3.434518651 + 1.285714286 = -2.148804365 x = -2.148804365 Simplifying x = -2.148804365Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.720232937, -2.148804365}
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