-9x^2+7x+1=0

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Solution for -9x^2+7x+1=0 equation:


Simplifying
-9x2 + 7x + 1 = 0

Reorder the terms:
1 + 7x + -9x2 = 0

Solving
1 + 7x + -9x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-9 the coefficient of the squared term: 

Divide each side by '-9'.
-0.1111111111 + -0.7777777778x + x2 = 0

Move the constant term to the right:

Add '0.1111111111' to each side of the equation.
-0.1111111111 + -0.7777777778x + 0.1111111111 + x2 = 0 + 0.1111111111

Reorder the terms:
-0.1111111111 + 0.1111111111 + -0.7777777778x + x2 = 0 + 0.1111111111

Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000
0.0000000000 + -0.7777777778x + x2 = 0 + 0.1111111111
-0.7777777778x + x2 = 0 + 0.1111111111

Combine like terms: 0 + 0.1111111111 = 0.1111111111
-0.7777777778x + x2 = 0.1111111111

The x term is -0.7777777778x.  Take half its coefficient (-0.3888888889).
Square it (0.1512345679) and add it to both sides.

Add '0.1512345679' to each side of the equation.
-0.7777777778x + 0.1512345679 + x2 = 0.1111111111 + 0.1512345679

Reorder the terms:
0.1512345679 + -0.7777777778x + x2 = 0.1111111111 + 0.1512345679

Combine like terms: 0.1111111111 + 0.1512345679 = 0.262345679
0.1512345679 + -0.7777777778x + x2 = 0.262345679

Factor a perfect square on the left side:
(x + -0.3888888889)(x + -0.3888888889) = 0.262345679

Calculate the square root of the right side: 0.512196914

Break this problem into two subproblems by setting 
(x + -0.3888888889) equal to 0.512196914 and -0.512196914.

Subproblem 1

x + -0.3888888889 = 0.512196914 Simplifying x + -0.3888888889 = 0.512196914 Reorder the terms: -0.3888888889 + x = 0.512196914 Solving -0.3888888889 + x = 0.512196914 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3888888889' to each side of the equation. -0.3888888889 + 0.3888888889 + x = 0.512196914 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + x = 0.512196914 + 0.3888888889 x = 0.512196914 + 0.3888888889 Combine like terms: 0.512196914 + 0.3888888889 = 0.9010858029 x = 0.9010858029 Simplifying x = 0.9010858029

Subproblem 2

x + -0.3888888889 = -0.512196914 Simplifying x + -0.3888888889 = -0.512196914 Reorder the terms: -0.3888888889 + x = -0.512196914 Solving -0.3888888889 + x = -0.512196914 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3888888889' to each side of the equation. -0.3888888889 + 0.3888888889 + x = -0.512196914 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + x = -0.512196914 + 0.3888888889 x = -0.512196914 + 0.3888888889 Combine like terms: -0.512196914 + 0.3888888889 = -0.1233080251 x = -0.1233080251 Simplifying x = -0.1233080251

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.9010858029, -0.1233080251}

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