4x^2-40x+43=0

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Solution for 4x^2-40x+43=0 equation:


Simplifying
4x2 + -40x + 43 = 0

Reorder the terms:
43 + -40x + 4x2 = 0

Solving
43 + -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'.
10.75 + -10x + x2 = 0

Move the constant term to the right:

Add '-10.75' to each side of the equation.
10.75 + -10x + -10.75 + x2 = 0 + -10.75

Reorder the terms:
10.75 + -10.75 + -10x + x2 = 0 + -10.75

Combine like terms: 10.75 + -10.75 = 0.00
0.00 + -10x + x2 = 0 + -10.75
-10x + x2 = 0 + -10.75

Combine like terms: 0 + -10.75 = -10.75
-10x + x2 = -10.75

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 = -10.75 + 25

Reorder the terms:
25 + -10x + x2 = -10.75 + 25

Combine like terms: -10.75 + 25 = 14.25
25 + -10x + x2 = 14.25

Factor a perfect square on the left side:
(x + -5)(x + -5) = 14.25

Calculate the square root of the right side: 3.774917218

Break this problem into two subproblems by setting 
(x + -5) equal to 3.774917218 and -3.774917218.

Subproblem 1

x + -5 = 3.774917218 Simplifying x + -5 = 3.774917218 Reorder the terms: -5 + x = 3.774917218 Solving -5 + x = 3.774917218 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 = 3.774917218 + 5 Combine like terms: -5 + 5 = 0 0 + x = 3.774917218 + 5 x = 3.774917218 + 5 Combine like terms: 3.774917218 + 5 = 8.774917218 x = 8.774917218 Simplifying x = 8.774917218

Subproblem 2

x + -5 = -3.774917218 Simplifying x + -5 = -3.774917218 Reorder the terms: -5 + x = -3.774917218 Solving -5 + x = -3.774917218 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 = -3.774917218 + 5 Combine like terms: -5 + 5 = 0 0 + x = -3.774917218 + 5 x = -3.774917218 + 5 Combine like terms: -3.774917218 + 5 = 1.225082782 x = 1.225082782 Simplifying x = 1.225082782

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.774917218, 1.225082782}

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