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Simplifying 7x2 + -18x + -16 = 0 Reorder the terms: -16 + -18x + 7x2 = 0 Solving -16 + -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'. -2.285714286 + -2.571428571x + x2 = 0 Move the constant term to the right: Add '2.285714286' to each side of the equation. -2.285714286 + -2.571428571x + 2.285714286 + x2 = 0 + 2.285714286 Reorder the terms: -2.285714286 + 2.285714286 + -2.571428571x + x2 = 0 + 2.285714286 Combine like terms: -2.285714286 + 2.285714286 = 0.000000000 0.000000000 + -2.571428571x + x2 = 0 + 2.285714286 -2.571428571x + x2 = 0 + 2.285714286 Combine like terms: 0 + 2.285714286 = 2.285714286 -2.571428571x + x2 = 2.285714286 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 = 2.285714286 + 1.653061225 Reorder the terms: 1.653061225 + -2.571428571x + x2 = 2.285714286 + 1.653061225 Combine like terms: 2.285714286 + 1.653061225 = 3.938775511 1.653061225 + -2.571428571x + x2 = 3.938775511 Factor a perfect square on the left side: (x + -1.285714286)(x + -1.285714286) = 3.938775511 Calculate the square root of the right side: 1.984634856 Break this problem into two subproblems by setting (x + -1.285714286) equal to 1.984634856 and -1.984634856.Subproblem 1
x + -1.285714286 = 1.984634856 Simplifying x + -1.285714286 = 1.984634856 Reorder the terms: -1.285714286 + x = 1.984634856 Solving -1.285714286 + x = 1.984634856 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 = 1.984634856 + 1.285714286 Combine like terms: -1.285714286 + 1.285714286 = 0.000000000 0.000000000 + x = 1.984634856 + 1.285714286 x = 1.984634856 + 1.285714286 Combine like terms: 1.984634856 + 1.285714286 = 3.270349142 x = 3.270349142 Simplifying x = 3.270349142Subproblem 2
x + -1.285714286 = -1.984634856 Simplifying x + -1.285714286 = -1.984634856 Reorder the terms: -1.285714286 + x = -1.984634856 Solving -1.285714286 + x = -1.984634856 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 = -1.984634856 + 1.285714286 Combine like terms: -1.285714286 + 1.285714286 = 0.000000000 0.000000000 + x = -1.984634856 + 1.285714286 x = -1.984634856 + 1.285714286 Combine like terms: -1.984634856 + 1.285714286 = -0.69892057 x = -0.69892057 Simplifying x = -0.69892057Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.270349142, -0.69892057}
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