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Simplifying -7x2 + -18x + 14 = 0 Reorder the terms: 14 + -18x + -7x2 = 0 Solving 14 + -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'. -2 + 2.571428571x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 2.571428571x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 2.571428571x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 2.571428571x + x2 = 0 + 2 2.571428571x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 2.571428571x + x2 = 2 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 = 2 + 1.653061225 Reorder the terms: 1.653061225 + 2.571428571x + x2 = 2 + 1.653061225 Combine like terms: 2 + 1.653061225 = 3.653061225 1.653061225 + 2.571428571x + x2 = 3.653061225 Factor a perfect square on the left side: (x + 1.285714286)(x + 1.285714286) = 3.653061225 Calculate the square root of the right side: 1.911298309 Break this problem into two subproblems by setting (x + 1.285714286) equal to 1.911298309 and -1.911298309.Subproblem 1
x + 1.285714286 = 1.911298309 Simplifying x + 1.285714286 = 1.911298309 Reorder the terms: 1.285714286 + x = 1.911298309 Solving 1.285714286 + x = 1.911298309 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 = 1.911298309 + -1.285714286 Combine like terms: 1.285714286 + -1.285714286 = 0.000000000 0.000000000 + x = 1.911298309 + -1.285714286 x = 1.911298309 + -1.285714286 Combine like terms: 1.911298309 + -1.285714286 = 0.625584023 x = 0.625584023 Simplifying x = 0.625584023Subproblem 2
x + 1.285714286 = -1.911298309 Simplifying x + 1.285714286 = -1.911298309 Reorder the terms: 1.285714286 + x = -1.911298309 Solving 1.285714286 + x = -1.911298309 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 = -1.911298309 + -1.285714286 Combine like terms: 1.285714286 + -1.285714286 = 0.000000000 0.000000000 + x = -1.911298309 + -1.285714286 x = -1.911298309 + -1.285714286 Combine like terms: -1.911298309 + -1.285714286 = -3.197012595 x = -3.197012595 Simplifying x = -3.197012595Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.625584023, -3.197012595}
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