7x^2-18x=8

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Solution for 7x^2-18x=8 equation:


Simplifying
7x2 + -18x = 8

Reorder the terms:
-18x + 7x2 = 8

Solving
-18x + 7x2 = 8

Solving for variable 'x'.

Reorder the terms:
-8 + -18x + 7x2 = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + -18x + 7x2 = 0

Begin completing the square.  Divide all terms by
7 the coefficient of the squared term: 

Divide each side by '7'.
-1.142857143 + -2.571428571x + x2 = 0

Move the constant term to the right:

Add '1.142857143' to each side of the equation.
-1.142857143 + -2.571428571x + 1.142857143 + x2 = 0 + 1.142857143

Reorder the terms:
-1.142857143 + 1.142857143 + -2.571428571x + x2 = 0 + 1.142857143

Combine like terms: -1.142857143 + 1.142857143 = 0.000000000
0.000000000 + -2.571428571x + x2 = 0 + 1.142857143
-2.571428571x + x2 = 0 + 1.142857143

Combine like terms: 0 + 1.142857143 = 1.142857143
-2.571428571x + x2 = 1.142857143

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 = 1.142857143 + 1.653061225

Reorder the terms:
1.653061225 + -2.571428571x + x2 = 1.142857143 + 1.653061225

Combine like terms: 1.142857143 + 1.653061225 = 2.795918368
1.653061225 + -2.571428571x + x2 = 2.795918368

Factor a perfect square on the left side:
(x + -1.285714286)(x + -1.285714286) = 2.795918368

Calculate the square root of the right side: 1.672099987

Break this problem into two subproblems by setting 
(x + -1.285714286) equal to 1.672099987 and -1.672099987.

Subproblem 1

x + -1.285714286 = 1.672099987 Simplifying x + -1.285714286 = 1.672099987 Reorder the terms: -1.285714286 + x = 1.672099987 Solving -1.285714286 + x = 1.672099987 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 = 1.672099987 + 1.285714286 Combine like terms: -1.285714286 + 1.285714286 = 0.000000000 0.000000000 + x = 1.672099987 + 1.285714286 x = 1.672099987 + 1.285714286 Combine like terms: 1.672099987 + 1.285714286 = 2.957814273 x = 2.957814273 Simplifying x = 2.957814273

Subproblem 2

x + -1.285714286 = -1.672099987 Simplifying x + -1.285714286 = -1.672099987 Reorder the terms: -1.285714286 + x = -1.672099987 Solving -1.285714286 + x = -1.672099987 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 = -1.672099987 + 1.285714286 Combine like terms: -1.285714286 + 1.285714286 = 0.000000000 0.000000000 + x = -1.672099987 + 1.285714286 x = -1.672099987 + 1.285714286 Combine like terms: -1.672099987 + 1.285714286 = -0.386385701 x = -0.386385701 Simplifying x = -0.386385701

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.957814273, -0.386385701}

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