0.7857142857=(x-9)x

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Solution for 0.7857142857=(x-9)x equation:


Simplifying
0.7857142857 = (x + -9) * x

Reorder the terms:
0.7857142857 = (-9 + x) * x

Reorder the terms for easier multiplication:
0.7857142857 = x(-9 + x)
0.7857142857 = (-9 * x + x * x)
0.7857142857 = (-9x + x2)

Solving
0.7857142857 = -9x + x2

Solving for variable 'x'.

Reorder the terms:
0.7857142857 + 9x + -1x2 = -9x + 9x + x2 + -1x2

Combine like terms: -9x + 9x = 0
0.7857142857 + 9x + -1x2 = 0 + x2 + -1x2
0.7857142857 + 9x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
0.7857142857 + 9x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-0.7857142857 + -9x + x2 = 0

Move the constant term to the right:

Add '0.7857142857' to each side of the equation.
-0.7857142857 + -9x + 0.7857142857 + x2 = 0 + 0.7857142857

Reorder the terms:
-0.7857142857 + 0.7857142857 + -9x + x2 = 0 + 0.7857142857

Combine like terms: -0.7857142857 + 0.7857142857 = 0.0000000000
0.0000000000 + -9x + x2 = 0 + 0.7857142857
-9x + x2 = 0 + 0.7857142857

Combine like terms: 0 + 0.7857142857 = 0.7857142857
-9x + x2 = 0.7857142857

The x term is -9x.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x + 20.25 + x2 = 0.7857142857 + 20.25

Reorder the terms:
20.25 + -9x + x2 = 0.7857142857 + 20.25

Combine like terms: 0.7857142857 + 20.25 = 21.0357142857
20.25 + -9x + x2 = 21.0357142857

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 21.0357142857

Calculate the square root of the right side: 4.586470788

Break this problem into two subproblems by setting 
(x + -4.5) equal to 4.586470788 and -4.586470788.

Subproblem 1

x + -4.5 = 4.586470788 Simplifying x + -4.5 = 4.586470788 Reorder the terms: -4.5 + x = 4.586470788 Solving -4.5 + x = 4.586470788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 4.586470788 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 4.586470788 + 4.5 x = 4.586470788 + 4.5 Combine like terms: 4.586470788 + 4.5 = 9.086470788 x = 9.086470788 Simplifying x = 9.086470788

Subproblem 2

x + -4.5 = -4.586470788 Simplifying x + -4.5 = -4.586470788 Reorder the terms: -4.5 + x = -4.586470788 Solving -4.5 + x = -4.586470788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -4.586470788 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -4.586470788 + 4.5 x = -4.586470788 + 4.5 Combine like terms: -4.586470788 + 4.5 = -0.086470788 x = -0.086470788 Simplifying x = -0.086470788

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.086470788, -0.086470788}

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