x^2-5x+4=6

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Solution for x^2-5x+4=6 equation:


Simplifying
x2 + -5x + 4 = 6

Reorder the terms:
4 + -5x + x2 = 6

Solving
4 + -5x + x2 = 6

Solving for variable 'x'.

Reorder the terms:
4 + -6 + -5x + x2 = 6 + -6

Combine like terms: 4 + -6 = -2
-2 + -5x + x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-2 + -5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -5x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + -5x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -5x + x2 = 0 + 2
-5x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
-5x + x2 = 2

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 2 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 2 + 6.25

Combine like terms: 2 + 6.25 = 8.25
6.25 + -5x + x2 = 8.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 8.25

Calculate the square root of the right side: 2.872281323

Break this problem into two subproblems by setting 
(x + -2.5) equal to 2.872281323 and -2.872281323.

Subproblem 1

x + -2.5 = 2.872281323 Simplifying x + -2.5 = 2.872281323 Reorder the terms: -2.5 + x = 2.872281323 Solving -2.5 + x = 2.872281323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 2.872281323 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.872281323 + 2.5 x = 2.872281323 + 2.5 Combine like terms: 2.872281323 + 2.5 = 5.372281323 x = 5.372281323 Simplifying x = 5.372281323

Subproblem 2

x + -2.5 = -2.872281323 Simplifying x + -2.5 = -2.872281323 Reorder the terms: -2.5 + x = -2.872281323 Solving -2.5 + x = -2.872281323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -2.872281323 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.872281323 + 2.5 x = -2.872281323 + 2.5 Combine like terms: -2.872281323 + 2.5 = -0.372281323 x = -0.372281323 Simplifying x = -0.372281323

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.372281323, -0.372281323}

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