9x+26x^2=3

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Solution for 9x+26x^2=3 equation:


Simplifying
9x + 26x2 = 3

Solving
9x + 26x2 = 3

Solving for variable 'x'.

Reorder the terms:
-3 + 9x + 26x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + 9x + 26x2 = 0

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

Divide each side by '26'.
-0.1153846154 + 0.3461538462x + x2 = 0

Move the constant term to the right:

Add '0.1153846154' to each side of the equation.
-0.1153846154 + 0.3461538462x + 0.1153846154 + x2 = 0 + 0.1153846154

Reorder the terms:
-0.1153846154 + 0.1153846154 + 0.3461538462x + x2 = 0 + 0.1153846154

Combine like terms: -0.1153846154 + 0.1153846154 = 0.0000000000
0.0000000000 + 0.3461538462x + x2 = 0 + 0.1153846154
0.3461538462x + x2 = 0 + 0.1153846154

Combine like terms: 0 + 0.1153846154 = 0.1153846154
0.3461538462x + x2 = 0.1153846154

The x term is 0.3461538462x.  Take half its coefficient (0.1730769231).
Square it (0.02995562131) and add it to both sides.

Add '0.02995562131' to each side of the equation.
0.3461538462x + 0.02995562131 + x2 = 0.1153846154 + 0.02995562131

Reorder the terms:
0.02995562131 + 0.3461538462x + x2 = 0.1153846154 + 0.02995562131

Combine like terms: 0.1153846154 + 0.02995562131 = 0.14534023671
0.02995562131 + 0.3461538462x + x2 = 0.14534023671

Factor a perfect square on the left side:
(x + 0.1730769231)(x + 0.1730769231) = 0.14534023671

Calculate the square root of the right side: 0.381235146

Break this problem into two subproblems by setting 
(x + 0.1730769231) equal to 0.381235146 and -0.381235146.

Subproblem 1

x + 0.1730769231 = 0.381235146 Simplifying x + 0.1730769231 = 0.381235146 Reorder the terms: 0.1730769231 + x = 0.381235146 Solving 0.1730769231 + x = 0.381235146 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1730769231' to each side of the equation. 0.1730769231 + -0.1730769231 + x = 0.381235146 + -0.1730769231 Combine like terms: 0.1730769231 + -0.1730769231 = 0.0000000000 0.0000000000 + x = 0.381235146 + -0.1730769231 x = 0.381235146 + -0.1730769231 Combine like terms: 0.381235146 + -0.1730769231 = 0.2081582229 x = 0.2081582229 Simplifying x = 0.2081582229

Subproblem 2

x + 0.1730769231 = -0.381235146 Simplifying x + 0.1730769231 = -0.381235146 Reorder the terms: 0.1730769231 + x = -0.381235146 Solving 0.1730769231 + x = -0.381235146 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1730769231' to each side of the equation. 0.1730769231 + -0.1730769231 + x = -0.381235146 + -0.1730769231 Combine like terms: 0.1730769231 + -0.1730769231 = 0.0000000000 0.0000000000 + x = -0.381235146 + -0.1730769231 x = -0.381235146 + -0.1730769231 Combine like terms: -0.381235146 + -0.1730769231 = -0.5543120691 x = -0.5543120691 Simplifying x = -0.5543120691

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.2081582229, -0.5543120691}

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