0.7x-0.9x(x-1)=-0.7

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Solution for 0.7x-0.9x(x-1)=-0.7 equation:


Simplifying
0.7x + -0.9x(x + -1) = -0.7

Reorder the terms:
0.7x + -0.9x(-1 + x) = -0.7
0.7x + (-1 * -0.9x + x * -0.9x) = -0.7
0.7x + (0.9x + -0.9x2) = -0.7

Combine like terms: 0.7x + 0.9x = 1.6x
1.6x + -0.9x2 = -0.7

Solving
1.6x + -0.9x2 = -0.7

Solving for variable 'x'.

Reorder the terms:
0.7 + 1.6x + -0.9x2 = -0.7 + 0.7

Combine like terms: -0.7 + 0.7 = 0.0
0.7 + 1.6x + -0.9x2 = 0.0

Begin completing the square.  Divide all terms by
-0.9 the coefficient of the squared term: 

Divide each side by '-0.9'.
-0.7777777778 + -1.777777778x + x2 = 0

Move the constant term to the right:

Add '0.7777777778' to each side of the equation.
-0.7777777778 + -1.777777778x + 0.7777777778 + x2 = 0 + 0.7777777778

Reorder the terms:
-0.7777777778 + 0.7777777778 + -1.777777778x + x2 = 0 + 0.7777777778

Combine like terms: -0.7777777778 + 0.7777777778 = 0.0000000000
0.0000000000 + -1.777777778x + x2 = 0 + 0.7777777778
-1.777777778x + x2 = 0 + 0.7777777778

Combine like terms: 0 + 0.7777777778 = 0.7777777778
-1.777777778x + x2 = 0.7777777778

The x term is -1.777777778x.  Take half its coefficient (-0.888888889).
Square it (0.7901234570) and add it to both sides.

Add '0.7901234570' to each side of the equation.
-1.777777778x + 0.7901234570 + x2 = 0.7777777778 + 0.7901234570

Reorder the terms:
0.7901234570 + -1.777777778x + x2 = 0.7777777778 + 0.7901234570

Combine like terms: 0.7777777778 + 0.7901234570 = 1.5679012348
0.7901234570 + -1.777777778x + x2 = 1.5679012348

Factor a perfect square on the left side:
(x + -0.888888889)(x + -0.888888889) = 1.5679012348

Calculate the square root of the right side: 1.25215863

Break this problem into two subproblems by setting 
(x + -0.888888889) equal to 1.25215863 and -1.25215863.

Subproblem 1

x + -0.888888889 = 1.25215863 Simplifying x + -0.888888889 = 1.25215863 Reorder the terms: -0.888888889 + x = 1.25215863 Solving -0.888888889 + x = 1.25215863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.888888889' to each side of the equation. -0.888888889 + 0.888888889 + x = 1.25215863 + 0.888888889 Combine like terms: -0.888888889 + 0.888888889 = 0.000000000 0.000000000 + x = 1.25215863 + 0.888888889 x = 1.25215863 + 0.888888889 Combine like terms: 1.25215863 + 0.888888889 = 2.141047519 x = 2.141047519 Simplifying x = 2.141047519

Subproblem 2

x + -0.888888889 = -1.25215863 Simplifying x + -0.888888889 = -1.25215863 Reorder the terms: -0.888888889 + x = -1.25215863 Solving -0.888888889 + x = -1.25215863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.888888889' to each side of the equation. -0.888888889 + 0.888888889 + x = -1.25215863 + 0.888888889 Combine like terms: -0.888888889 + 0.888888889 = 0.000000000 0.000000000 + x = -1.25215863 + 0.888888889 x = -1.25215863 + 0.888888889 Combine like terms: -1.25215863 + 0.888888889 = -0.363269741 x = -0.363269741 Simplifying x = -0.363269741

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.141047519, -0.363269741}

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