2x(x-5)=6+(x-1)

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Solution for 2x(x-5)=6+(x-1) equation:


Simplifying
2x(x + -5) = 6 + (x + -1)

Reorder the terms:
2x(-5 + x) = 6 + (x + -1)
(-5 * 2x + x * 2x) = 6 + (x + -1)
(-10x + 2x2) = 6 + (x + -1)

Reorder the terms:
-10x + 2x2 = 6 + (-1 + x)

Remove parenthesis around (-1 + x)
-10x + 2x2 = 6 + -1 + x

Combine like terms: 6 + -1 = 5
-10x + 2x2 = 5 + x

Solving
-10x + 2x2 = 5 + x

Solving for variable 'x'.

Reorder the terms:
-5 + -10x + -1x + 2x2 = 5 + x + -5 + -1x

Combine like terms: -10x + -1x = -11x
-5 + -11x + 2x2 = 5 + x + -5 + -1x

Reorder the terms:
-5 + -11x + 2x2 = 5 + -5 + x + -1x

Combine like terms: 5 + -5 = 0
-5 + -11x + 2x2 = 0 + x + -1x
-5 + -11x + 2x2 = x + -1x

Combine like terms: x + -1x = 0
-5 + -11x + 2x2 = 0

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

Divide each side by '2'.
-2.5 + -5.5x + x2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + -5.5x + 2.5 + x2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + -5.5x + x2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + -5.5x + x2 = 0 + 2.5
-5.5x + x2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
-5.5x + x2 = 2.5

The x term is -5.5x.  Take half its coefficient (-2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
-5.5x + 7.5625 + x2 = 2.5 + 7.5625

Reorder the terms:
7.5625 + -5.5x + x2 = 2.5 + 7.5625

Combine like terms: 2.5 + 7.5625 = 10.0625
7.5625 + -5.5x + x2 = 10.0625

Factor a perfect square on the left side:
(x + -2.75)(x + -2.75) = 10.0625

Calculate the square root of the right side: 3.172144385

Break this problem into two subproblems by setting 
(x + -2.75) equal to 3.172144385 and -3.172144385.

Subproblem 1

x + -2.75 = 3.172144385 Simplifying x + -2.75 = 3.172144385 Reorder the terms: -2.75 + x = 3.172144385 Solving -2.75 + x = 3.172144385 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = 3.172144385 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = 3.172144385 + 2.75 x = 3.172144385 + 2.75 Combine like terms: 3.172144385 + 2.75 = 5.922144385 x = 5.922144385 Simplifying x = 5.922144385

Subproblem 2

x + -2.75 = -3.172144385 Simplifying x + -2.75 = -3.172144385 Reorder the terms: -2.75 + x = -3.172144385 Solving -2.75 + x = -3.172144385 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = -3.172144385 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = -3.172144385 + 2.75 x = -3.172144385 + 2.75 Combine like terms: -3.172144385 + 2.75 = -0.422144385 x = -0.422144385 Simplifying x = -0.422144385

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.922144385, -0.422144385}

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