5x^2-38x+8=0

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Solution for 5x^2-38x+8=0 equation:


Simplifying
5x2 + -38x + 8 = 0

Reorder the terms:
8 + -38x + 5x2 = 0

Solving
8 + -38x + 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'.
1.6 + -7.6x + x2 = 0

Move the constant term to the right:

Add '-1.6' to each side of the equation.
1.6 + -7.6x + -1.6 + x2 = 0 + -1.6

Reorder the terms:
1.6 + -1.6 + -7.6x + x2 = 0 + -1.6

Combine like terms: 1.6 + -1.6 = 0.0
0.0 + -7.6x + x2 = 0 + -1.6
-7.6x + x2 = 0 + -1.6

Combine like terms: 0 + -1.6 = -1.6
-7.6x + x2 = -1.6

The x term is -7.6x.  Take half its coefficient (-3.8).
Square it (14.44) and add it to both sides.

Add '14.44' to each side of the equation.
-7.6x + 14.44 + x2 = -1.6 + 14.44

Reorder the terms:
14.44 + -7.6x + x2 = -1.6 + 14.44

Combine like terms: -1.6 + 14.44 = 12.84
14.44 + -7.6x + x2 = 12.84

Factor a perfect square on the left side:
(x + -3.8)(x + -3.8) = 12.84

Calculate the square root of the right side: 3.583294573

Break this problem into two subproblems by setting 
(x + -3.8) equal to 3.583294573 and -3.583294573.

Subproblem 1

x + -3.8 = 3.583294573 Simplifying x + -3.8 = 3.583294573 Reorder the terms: -3.8 + x = 3.583294573 Solving -3.8 + x = 3.583294573 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.8' to each side of the equation. -3.8 + 3.8 + x = 3.583294573 + 3.8 Combine like terms: -3.8 + 3.8 = 0.0 0.0 + x = 3.583294573 + 3.8 x = 3.583294573 + 3.8 Combine like terms: 3.583294573 + 3.8 = 7.383294573 x = 7.383294573 Simplifying x = 7.383294573

Subproblem 2

x + -3.8 = -3.583294573 Simplifying x + -3.8 = -3.583294573 Reorder the terms: -3.8 + x = -3.583294573 Solving -3.8 + x = -3.583294573 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.8' to each side of the equation. -3.8 + 3.8 + x = -3.583294573 + 3.8 Combine like terms: -3.8 + 3.8 = 0.0 0.0 + x = -3.583294573 + 3.8 x = -3.583294573 + 3.8 Combine like terms: -3.583294573 + 3.8 = 0.216705427 x = 0.216705427 Simplifying x = 0.216705427

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.383294573, 0.216705427}

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