81x^2+90x+25=2

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Solution for 81x^2+90x+25=2 equation:


Simplifying
81x2 + 90x + 25 = 2

Reorder the terms:
25 + 90x + 81x2 = 2

Solving
25 + 90x + 81x2 = 2

Solving for variable 'x'.

Reorder the terms:
25 + -2 + 90x + 81x2 = 2 + -2

Combine like terms: 25 + -2 = 23
23 + 90x + 81x2 = 2 + -2

Combine like terms: 2 + -2 = 0
23 + 90x + 81x2 = 0

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

Divide each side by '81'.
0.2839506173 + 1.111111111x + x2 = 0

Move the constant term to the right:

Add '-0.2839506173' to each side of the equation.
0.2839506173 + 1.111111111x + -0.2839506173 + x2 = 0 + -0.2839506173

Reorder the terms:
0.2839506173 + -0.2839506173 + 1.111111111x + x2 = 0 + -0.2839506173

Combine like terms: 0.2839506173 + -0.2839506173 = 0.0000000000
0.0000000000 + 1.111111111x + x2 = 0 + -0.2839506173
1.111111111x + x2 = 0 + -0.2839506173

Combine like terms: 0 + -0.2839506173 = -0.2839506173
1.111111111x + x2 = -0.2839506173

The x term is 1.111111111x.  Take half its coefficient (0.5555555555).
Square it (0.3086419752) and add it to both sides.

Add '0.3086419752' to each side of the equation.
1.111111111x + 0.3086419752 + x2 = -0.2839506173 + 0.3086419752

Reorder the terms:
0.3086419752 + 1.111111111x + x2 = -0.2839506173 + 0.3086419752

Combine like terms: -0.2839506173 + 0.3086419752 = 0.0246913579
0.3086419752 + 1.111111111x + x2 = 0.0246913579

Factor a perfect square on the left side:
(x + 0.5555555555)(x + 0.5555555555) = 0.0246913579

Calculate the square root of the right side: 0.15713484

Break this problem into two subproblems by setting 
(x + 0.5555555555) equal to 0.15713484 and -0.15713484.

Subproblem 1

x + 0.5555555555 = 0.15713484 Simplifying x + 0.5555555555 = 0.15713484 Reorder the terms: 0.5555555555 + x = 0.15713484 Solving 0.5555555555 + x = 0.15713484 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5555555555' to each side of the equation. 0.5555555555 + -0.5555555555 + x = 0.15713484 + -0.5555555555 Combine like terms: 0.5555555555 + -0.5555555555 = 0.0000000000 0.0000000000 + x = 0.15713484 + -0.5555555555 x = 0.15713484 + -0.5555555555 Combine like terms: 0.15713484 + -0.5555555555 = -0.3984207155 x = -0.3984207155 Simplifying x = -0.3984207155

Subproblem 2

x + 0.5555555555 = -0.15713484 Simplifying x + 0.5555555555 = -0.15713484 Reorder the terms: 0.5555555555 + x = -0.15713484 Solving 0.5555555555 + x = -0.15713484 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5555555555' to each side of the equation. 0.5555555555 + -0.5555555555 + x = -0.15713484 + -0.5555555555 Combine like terms: 0.5555555555 + -0.5555555555 = 0.0000000000 0.0000000000 + x = -0.15713484 + -0.5555555555 x = -0.15713484 + -0.5555555555 Combine like terms: -0.15713484 + -0.5555555555 = -0.7126903955 x = -0.7126903955 Simplifying x = -0.7126903955

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.3984207155, -0.7126903955}

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