20x^2-18x+3=0

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Solution for 20x^2-18x+3=0 equation:


Simplifying
20x2 + -18x + 3 = 0

Reorder the terms:
3 + -18x + 20x2 = 0

Solving
3 + -18x + 20x2 = 0

Solving for variable 'x'.

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

Divide each side by '20'.
0.15 + -0.9x + x2 = 0

Move the constant term to the right:

Add '-0.15' to each side of the equation.
0.15 + -0.9x + -0.15 + x2 = 0 + -0.15

Reorder the terms:
0.15 + -0.15 + -0.9x + x2 = 0 + -0.15

Combine like terms: 0.15 + -0.15 = 0.00
0.00 + -0.9x + x2 = 0 + -0.15
-0.9x + x2 = 0 + -0.15

Combine like terms: 0 + -0.15 = -0.15
-0.9x + x2 = -0.15

The x term is -0.9x.  Take half its coefficient (-0.45).
Square it (0.2025) and add it to both sides.

Add '0.2025' to each side of the equation.
-0.9x + 0.2025 + x2 = -0.15 + 0.2025

Reorder the terms:
0.2025 + -0.9x + x2 = -0.15 + 0.2025

Combine like terms: -0.15 + 0.2025 = 0.0525
0.2025 + -0.9x + x2 = 0.0525

Factor a perfect square on the left side:
(x + -0.45)(x + -0.45) = 0.0525

Calculate the square root of the right side: 0.229128785

Break this problem into two subproblems by setting 
(x + -0.45) equal to 0.229128785 and -0.229128785.

Subproblem 1

x + -0.45 = 0.229128785 Simplifying x + -0.45 = 0.229128785 Reorder the terms: -0.45 + x = 0.229128785 Solving -0.45 + x = 0.229128785 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.45' to each side of the equation. -0.45 + 0.45 + x = 0.229128785 + 0.45 Combine like terms: -0.45 + 0.45 = 0.00 0.00 + x = 0.229128785 + 0.45 x = 0.229128785 + 0.45 Combine like terms: 0.229128785 + 0.45 = 0.679128785 x = 0.679128785 Simplifying x = 0.679128785

Subproblem 2

x + -0.45 = -0.229128785 Simplifying x + -0.45 = -0.229128785 Reorder the terms: -0.45 + x = -0.229128785 Solving -0.45 + x = -0.229128785 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.45' to each side of the equation. -0.45 + 0.45 + x = -0.229128785 + 0.45 Combine like terms: -0.45 + 0.45 = 0.00 0.00 + x = -0.229128785 + 0.45 x = -0.229128785 + 0.45 Combine like terms: -0.229128785 + 0.45 = 0.220871215 x = 0.220871215 Simplifying x = 0.220871215

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.679128785, 0.220871215}

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