2x+18x^2=21

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Solution for 2x+18x^2=21 equation:


Simplifying
2x + 18x2 = 21

Solving
2x + 18x2 = 21

Solving for variable 'x'.

Reorder the terms:
-21 + 2x + 18x2 = 21 + -21

Combine like terms: 21 + -21 = 0
-21 + 2x + 18x2 = 0

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

Divide each side by '18'.
-1.166666667 + 0.1111111111x + x2 = 0

Move the constant term to the right:

Add '1.166666667' to each side of the equation.
-1.166666667 + 0.1111111111x + 1.166666667 + x2 = 0 + 1.166666667

Reorder the terms:
-1.166666667 + 1.166666667 + 0.1111111111x + x2 = 0 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + 0.1111111111x + x2 = 0 + 1.166666667
0.1111111111x + x2 = 0 + 1.166666667

Combine like terms: 0 + 1.166666667 = 1.166666667
0.1111111111x + x2 = 1.166666667

The x term is 0.1111111111x.  Take half its coefficient (0.05555555555).
Square it (0.003086419752) and add it to both sides.

Add '0.003086419752' to each side of the equation.
0.1111111111x + 0.003086419752 + x2 = 1.166666667 + 0.003086419752

Reorder the terms:
0.003086419752 + 0.1111111111x + x2 = 1.166666667 + 0.003086419752

Combine like terms: 1.166666667 + 0.003086419752 = 1.169753086752
0.003086419752 + 0.1111111111x + x2 = 1.169753086752

Factor a perfect square on the left side:
(x + 0.05555555555)(x + 0.05555555555) = 1.169753086752

Calculate the square root of the right side: 1.081551241

Break this problem into two subproblems by setting 
(x + 0.05555555555) equal to 1.081551241 and -1.081551241.

Subproblem 1

x + 0.05555555555 = 1.081551241 Simplifying x + 0.05555555555 = 1.081551241 Reorder the terms: 0.05555555555 + x = 1.081551241 Solving 0.05555555555 + x = 1.081551241 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.05555555555' to each side of the equation. 0.05555555555 + -0.05555555555 + x = 1.081551241 + -0.05555555555 Combine like terms: 0.05555555555 + -0.05555555555 = 0.00000000000 0.00000000000 + x = 1.081551241 + -0.05555555555 x = 1.081551241 + -0.05555555555 Combine like terms: 1.081551241 + -0.05555555555 = 1.02599568545 x = 1.02599568545 Simplifying x = 1.02599568545

Subproblem 2

x + 0.05555555555 = -1.081551241 Simplifying x + 0.05555555555 = -1.081551241 Reorder the terms: 0.05555555555 + x = -1.081551241 Solving 0.05555555555 + x = -1.081551241 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.05555555555' to each side of the equation. 0.05555555555 + -0.05555555555 + x = -1.081551241 + -0.05555555555 Combine like terms: 0.05555555555 + -0.05555555555 = 0.00000000000 0.00000000000 + x = -1.081551241 + -0.05555555555 x = -1.081551241 + -0.05555555555 Combine like terms: -1.081551241 + -0.05555555555 = -1.13710679655 x = -1.13710679655 Simplifying x = -1.13710679655

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.02599568545, -1.13710679655}

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