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Simplifying -7x2 = 18x + -11 Reorder the terms: -7x2 = -11 + 18x Solving -7x2 = -11 + 18x Solving for variable 'x'. Reorder the terms: 11 + -18x + -7x2 = -11 + 18x + 11 + -18x Reorder the terms: 11 + -18x + -7x2 = -11 + 11 + 18x + -18x Combine like terms: -11 + 11 = 0 11 + -18x + -7x2 = 0 + 18x + -18x 11 + -18x + -7x2 = 18x + -18x Combine like terms: 18x + -18x = 0 11 + -18x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -1.571428571 + 2.571428571x + x2 = 0 Move the constant term to the right: Add '1.571428571' to each side of the equation. -1.571428571 + 2.571428571x + 1.571428571 + x2 = 0 + 1.571428571 Reorder the terms: -1.571428571 + 1.571428571 + 2.571428571x + x2 = 0 + 1.571428571 Combine like terms: -1.571428571 + 1.571428571 = 0.000000000 0.000000000 + 2.571428571x + x2 = 0 + 1.571428571 2.571428571x + x2 = 0 + 1.571428571 Combine like terms: 0 + 1.571428571 = 1.571428571 2.571428571x + x2 = 1.571428571 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 = 1.571428571 + 1.653061225 Reorder the terms: 1.653061225 + 2.571428571x + x2 = 1.571428571 + 1.653061225 Combine like terms: 1.571428571 + 1.653061225 = 3.224489796 1.653061225 + 2.571428571x + x2 = 3.224489796 Factor a perfect square on the left side: (x + 1.285714286)(x + 1.285714286) = 3.224489796 Calculate the square root of the right side: 1.795686441 Break this problem into two subproblems by setting (x + 1.285714286) equal to 1.795686441 and -1.795686441.Subproblem 1
x + 1.285714286 = 1.795686441 Simplifying x + 1.285714286 = 1.795686441 Reorder the terms: 1.285714286 + x = 1.795686441 Solving 1.285714286 + x = 1.795686441 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 = 1.795686441 + -1.285714286 Combine like terms: 1.285714286 + -1.285714286 = 0.000000000 0.000000000 + x = 1.795686441 + -1.285714286 x = 1.795686441 + -1.285714286 Combine like terms: 1.795686441 + -1.285714286 = 0.509972155 x = 0.509972155 Simplifying x = 0.509972155Subproblem 2
x + 1.285714286 = -1.795686441 Simplifying x + 1.285714286 = -1.795686441 Reorder the terms: 1.285714286 + x = -1.795686441 Solving 1.285714286 + x = -1.795686441 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 = -1.795686441 + -1.285714286 Combine like terms: 1.285714286 + -1.285714286 = 0.000000000 0.000000000 + x = -1.795686441 + -1.285714286 x = -1.795686441 + -1.285714286 Combine like terms: -1.795686441 + -1.285714286 = -3.081400727 x = -3.081400727 Simplifying x = -3.081400727Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.509972155, -3.081400727}
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