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Simplifying 7x2 = 18x + -1 Reorder the terms: 7x2 = -1 + 18x Solving 7x2 = -1 + 18x Solving for variable 'x'. Reorder the terms: 1 + -18x + 7x2 = -1 + 18x + 1 + -18x Reorder the terms: 1 + -18x + 7x2 = -1 + 1 + 18x + -18x Combine like terms: -1 + 1 = 0 1 + -18x + 7x2 = 0 + 18x + -18x 1 + -18x + 7x2 = 18x + -18x Combine like terms: 18x + -18x = 0 1 + -18x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.1428571429 + -2.571428571x + x2 = 0 Move the constant term to the right: Add '-0.1428571429' to each side of the equation. 0.1428571429 + -2.571428571x + -0.1428571429 + x2 = 0 + -0.1428571429 Reorder the terms: 0.1428571429 + -0.1428571429 + -2.571428571x + x2 = 0 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + -2.571428571x + x2 = 0 + -0.1428571429 -2.571428571x + x2 = 0 + -0.1428571429 Combine like terms: 0 + -0.1428571429 = -0.1428571429 -2.571428571x + x2 = -0.1428571429 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 = -0.1428571429 + 1.653061225 Reorder the terms: 1.653061225 + -2.571428571x + x2 = -0.1428571429 + 1.653061225 Combine like terms: -0.1428571429 + 1.653061225 = 1.5102040821 1.653061225 + -2.571428571x + x2 = 1.5102040821 Factor a perfect square on the left side: (x + -1.285714286)(x + -1.285714286) = 1.5102040821 Calculate the square root of the right side: 1.22890361 Break this problem into two subproblems by setting (x + -1.285714286) equal to 1.22890361 and -1.22890361.Subproblem 1
x + -1.285714286 = 1.22890361 Simplifying x + -1.285714286 = 1.22890361 Reorder the terms: -1.285714286 + x = 1.22890361 Solving -1.285714286 + x = 1.22890361 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 = 1.22890361 + 1.285714286 Combine like terms: -1.285714286 + 1.285714286 = 0.000000000 0.000000000 + x = 1.22890361 + 1.285714286 x = 1.22890361 + 1.285714286 Combine like terms: 1.22890361 + 1.285714286 = 2.514617896 x = 2.514617896 Simplifying x = 2.514617896Subproblem 2
x + -1.285714286 = -1.22890361 Simplifying x + -1.285714286 = -1.22890361 Reorder the terms: -1.285714286 + x = -1.22890361 Solving -1.285714286 + x = -1.22890361 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 = -1.22890361 + 1.285714286 Combine like terms: -1.285714286 + 1.285714286 = 0.000000000 0.000000000 + x = -1.22890361 + 1.285714286 x = -1.22890361 + 1.285714286 Combine like terms: -1.22890361 + 1.285714286 = 0.056810676 x = 0.056810676 Simplifying x = 0.056810676Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.514617896, 0.056810676}
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