9x^2-5-3x=-1

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Solution for 9x^2-5-3x=-1 equation:


Simplifying
9x2 + -5 + -3x = -1

Reorder the terms:
-5 + -3x + 9x2 = -1

Solving
-5 + -3x + 9x2 = -1

Solving for variable 'x'.

Reorder the terms:
-5 + 1 + -3x + 9x2 = -1 + 1

Combine like terms: -5 + 1 = -4
-4 + -3x + 9x2 = -1 + 1

Combine like terms: -1 + 1 = 0
-4 + -3x + 9x2 = 0

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

Divide each side by '9'.
-0.4444444444 + -0.3333333333x + x2 = 0

Move the constant term to the right:

Add '0.4444444444' to each side of the equation.
-0.4444444444 + -0.3333333333x + 0.4444444444 + x2 = 0 + 0.4444444444

Reorder the terms:
-0.4444444444 + 0.4444444444 + -0.3333333333x + x2 = 0 + 0.4444444444

Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000
0.0000000000 + -0.3333333333x + x2 = 0 + 0.4444444444
-0.3333333333x + x2 = 0 + 0.4444444444

Combine like terms: 0 + 0.4444444444 = 0.4444444444
-0.3333333333x + x2 = 0.4444444444

The x term is -0.3333333333x.  Take half its coefficient (-0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
-0.3333333333x + 0.02777777779 + x2 = 0.4444444444 + 0.02777777779

Reorder the terms:
0.02777777779 + -0.3333333333x + x2 = 0.4444444444 + 0.02777777779

Combine like terms: 0.4444444444 + 0.02777777779 = 0.47222222219
0.02777777779 + -0.3333333333x + x2 = 0.47222222219

Factor a perfect square on the left side:
(x + -0.1666666667)(x + -0.1666666667) = 0.47222222219

Calculate the square root of the right side: 0.687184271

Break this problem into two subproblems by setting 
(x + -0.1666666667) equal to 0.687184271 and -0.687184271.

Subproblem 1

x + -0.1666666667 = 0.687184271 Simplifying x + -0.1666666667 = 0.687184271 Reorder the terms: -0.1666666667 + x = 0.687184271 Solving -0.1666666667 + x = 0.687184271 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = 0.687184271 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = 0.687184271 + 0.1666666667 x = 0.687184271 + 0.1666666667 Combine like terms: 0.687184271 + 0.1666666667 = 0.8538509377 x = 0.8538509377 Simplifying x = 0.8538509377

Subproblem 2

x + -0.1666666667 = -0.687184271 Simplifying x + -0.1666666667 = -0.687184271 Reorder the terms: -0.1666666667 + x = -0.687184271 Solving -0.1666666667 + x = -0.687184271 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = -0.687184271 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = -0.687184271 + 0.1666666667 x = -0.687184271 + 0.1666666667 Combine like terms: -0.687184271 + 0.1666666667 = -0.5205176043 x = -0.5205176043 Simplifying x = -0.5205176043

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.8538509377, -0.5205176043}

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