5x^2-44x+21=0

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Solution for 5x^2-44x+21=0 equation:


Simplifying
5x2 + -44x + 21 = 0

Reorder the terms:
21 + -44x + 5x2 = 0

Solving
21 + -44x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
4.2 + -8.8x + x2 = 0

Move the constant term to the right:

Add '-4.2' to each side of the equation.
4.2 + -8.8x + -4.2 + x2 = 0 + -4.2

Reorder the terms:
4.2 + -4.2 + -8.8x + x2 = 0 + -4.2

Combine like terms: 4.2 + -4.2 = 0.0
0.0 + -8.8x + x2 = 0 + -4.2
-8.8x + x2 = 0 + -4.2

Combine like terms: 0 + -4.2 = -4.2
-8.8x + x2 = -4.2

The x term is -8.8x.  Take half its coefficient (-4.4).
Square it (19.36) and add it to both sides.

Add '19.36' to each side of the equation.
-8.8x + 19.36 + x2 = -4.2 + 19.36

Reorder the terms:
19.36 + -8.8x + x2 = -4.2 + 19.36

Combine like terms: -4.2 + 19.36 = 15.16
19.36 + -8.8x + x2 = 15.16

Factor a perfect square on the left side:
(x + -4.4)(x + -4.4) = 15.16

Calculate the square root of the right side: 3.893584467

Break this problem into two subproblems by setting 
(x + -4.4) equal to 3.893584467 and -3.893584467.

Subproblem 1

x + -4.4 = 3.893584467 Simplifying x + -4.4 = 3.893584467 Reorder the terms: -4.4 + x = 3.893584467 Solving -4.4 + x = 3.893584467 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.4' to each side of the equation. -4.4 + 4.4 + x = 3.893584467 + 4.4 Combine like terms: -4.4 + 4.4 = 0.0 0.0 + x = 3.893584467 + 4.4 x = 3.893584467 + 4.4 Combine like terms: 3.893584467 + 4.4 = 8.293584467 x = 8.293584467 Simplifying x = 8.293584467

Subproblem 2

x + -4.4 = -3.893584467 Simplifying x + -4.4 = -3.893584467 Reorder the terms: -4.4 + x = -3.893584467 Solving -4.4 + x = -3.893584467 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.4' to each side of the equation. -4.4 + 4.4 + x = -3.893584467 + 4.4 Combine like terms: -4.4 + 4.4 = 0.0 0.0 + x = -3.893584467 + 4.4 x = -3.893584467 + 4.4 Combine like terms: -3.893584467 + 4.4 = 0.506415533 x = 0.506415533 Simplifying x = 0.506415533

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.293584467, 0.506415533}

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