4x^2-40x+55=0

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Solution for 4x^2-40x+55=0 equation:


Simplifying
4x2 + -40x + 55 = 0

Reorder the terms:
55 + -40x + 4x2 = 0

Solving
55 + -40x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
13.75 + -10x + x2 = 0

Move the constant term to the right:

Add '-13.75' to each side of the equation.
13.75 + -10x + -13.75 + x2 = 0 + -13.75

Reorder the terms:
13.75 + -13.75 + -10x + x2 = 0 + -13.75

Combine like terms: 13.75 + -13.75 = 0.00
0.00 + -10x + x2 = 0 + -13.75
-10x + x2 = 0 + -13.75

Combine like terms: 0 + -13.75 = -13.75
-10x + x2 = -13.75

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = -13.75 + 25

Reorder the terms:
25 + -10x + x2 = -13.75 + 25

Combine like terms: -13.75 + 25 = 11.25
25 + -10x + x2 = 11.25

Factor a perfect square on the left side:
(x + -5)(x + -5) = 11.25

Calculate the square root of the right side: 3.354101966

Break this problem into two subproblems by setting 
(x + -5) equal to 3.354101966 and -3.354101966.

Subproblem 1

x + -5 = 3.354101966 Simplifying x + -5 = 3.354101966 Reorder the terms: -5 + x = 3.354101966 Solving -5 + x = 3.354101966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 3.354101966 + 5 Combine like terms: -5 + 5 = 0 0 + x = 3.354101966 + 5 x = 3.354101966 + 5 Combine like terms: 3.354101966 + 5 = 8.354101966 x = 8.354101966 Simplifying x = 8.354101966

Subproblem 2

x + -5 = -3.354101966 Simplifying x + -5 = -3.354101966 Reorder the terms: -5 + x = -3.354101966 Solving -5 + x = -3.354101966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -3.354101966 + 5 Combine like terms: -5 + 5 = 0 0 + x = -3.354101966 + 5 x = -3.354101966 + 5 Combine like terms: -3.354101966 + 5 = 1.645898034 x = 1.645898034 Simplifying x = 1.645898034

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.354101966, 1.645898034}

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