x^2-5.1x+2.34=0

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Solution for x^2-5.1x+2.34=0 equation:


Simplifying
x2 + -5.1x + 2.34 = 0

Reorder the terms:
2.34 + -5.1x + x2 = 0

Solving
2.34 + -5.1x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-2.34' to each side of the equation.
2.34 + -5.1x + -2.34 + x2 = 0 + -2.34

Reorder the terms:
2.34 + -2.34 + -5.1x + x2 = 0 + -2.34

Combine like terms: 2.34 + -2.34 = 0.00
0.00 + -5.1x + x2 = 0 + -2.34
-5.1x + x2 = 0 + -2.34

Combine like terms: 0 + -2.34 = -2.34
-5.1x + x2 = -2.34

The x term is -5.1x.  Take half its coefficient (-2.55).
Square it (6.5025) and add it to both sides.

Add '6.5025' to each side of the equation.
-5.1x + 6.5025 + x2 = -2.34 + 6.5025

Reorder the terms:
6.5025 + -5.1x + x2 = -2.34 + 6.5025

Combine like terms: -2.34 + 6.5025 = 4.1625
6.5025 + -5.1x + x2 = 4.1625

Factor a perfect square on the left side:
(x + -2.55)(x + -2.55) = 4.1625

Calculate the square root of the right side: 2.040220576

Break this problem into two subproblems by setting 
(x + -2.55) equal to 2.040220576 and -2.040220576.

Subproblem 1

x + -2.55 = 2.040220576 Simplifying x + -2.55 = 2.040220576 Reorder the terms: -2.55 + x = 2.040220576 Solving -2.55 + x = 2.040220576 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.55' to each side of the equation. -2.55 + 2.55 + x = 2.040220576 + 2.55 Combine like terms: -2.55 + 2.55 = 0.00 0.00 + x = 2.040220576 + 2.55 x = 2.040220576 + 2.55 Combine like terms: 2.040220576 + 2.55 = 4.590220576 x = 4.590220576 Simplifying x = 4.590220576

Subproblem 2

x + -2.55 = -2.040220576 Simplifying x + -2.55 = -2.040220576 Reorder the terms: -2.55 + x = -2.040220576 Solving -2.55 + x = -2.040220576 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.55' to each side of the equation. -2.55 + 2.55 + x = -2.040220576 + 2.55 Combine like terms: -2.55 + 2.55 = 0.00 0.00 + x = -2.040220576 + 2.55 x = -2.040220576 + 2.55 Combine like terms: -2.040220576 + 2.55 = 0.509779424 x = 0.509779424 Simplifying x = 0.509779424

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.590220576, 0.509779424}

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