5x^2-40x+6=0

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Solution for 5x^2-40x+6=0 equation:


Simplifying
5x2 + -40x + 6 = 0

Reorder the terms:
6 + -40x + 5x2 = 0

Solving
6 + -40x + 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'.
1.2 + -8x + x2 = 0

Move the constant term to the right:

Add '-1.2' to each side of the equation.
1.2 + -8x + -1.2 + x2 = 0 + -1.2

Reorder the terms:
1.2 + -1.2 + -8x + x2 = 0 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + -8x + x2 = 0 + -1.2
-8x + x2 = 0 + -1.2

Combine like terms: 0 + -1.2 = -1.2
-8x + x2 = -1.2

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = -1.2 + 16

Reorder the terms:
16 + -8x + x2 = -1.2 + 16

Combine like terms: -1.2 + 16 = 14.8
16 + -8x + x2 = 14.8

Factor a perfect square on the left side:
(x + -4)(x + -4) = 14.8

Calculate the square root of the right side: 3.847076812

Break this problem into two subproblems by setting 
(x + -4) equal to 3.847076812 and -3.847076812.

Subproblem 1

x + -4 = 3.847076812 Simplifying x + -4 = 3.847076812 Reorder the terms: -4 + x = 3.847076812 Solving -4 + x = 3.847076812 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 3.847076812 + 4 Combine like terms: -4 + 4 = 0 0 + x = 3.847076812 + 4 x = 3.847076812 + 4 Combine like terms: 3.847076812 + 4 = 7.847076812 x = 7.847076812 Simplifying x = 7.847076812

Subproblem 2

x + -4 = -3.847076812 Simplifying x + -4 = -3.847076812 Reorder the terms: -4 + x = -3.847076812 Solving -4 + x = -3.847076812 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -3.847076812 + 4 Combine like terms: -4 + 4 = 0 0 + x = -3.847076812 + 4 x = -3.847076812 + 4 Combine like terms: -3.847076812 + 4 = 0.152923188 x = 0.152923188 Simplifying x = 0.152923188

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.847076812, 0.152923188}

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