4x-11=(2x-5)(x-3)

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Solution for 4x-11=(2x-5)(x-3) equation:


Simplifying
4x + -11 = (2x + -5)(x + -3)

Reorder the terms:
-11 + 4x = (2x + -5)(x + -3)

Reorder the terms:
-11 + 4x = (-5 + 2x)(x + -3)

Reorder the terms:
-11 + 4x = (-5 + 2x)(-3 + x)

Multiply (-5 + 2x) * (-3 + x)
-11 + 4x = (-5(-3 + x) + 2x * (-3 + x))
-11 + 4x = ((-3 * -5 + x * -5) + 2x * (-3 + x))
-11 + 4x = ((15 + -5x) + 2x * (-3 + x))
-11 + 4x = (15 + -5x + (-3 * 2x + x * 2x))
-11 + 4x = (15 + -5x + (-6x + 2x2))

Combine like terms: -5x + -6x = -11x
-11 + 4x = (15 + -11x + 2x2)

Solving
-11 + 4x = 15 + -11x + 2x2

Solving for variable 'x'.

Reorder the terms:
-11 + -15 + 4x + 11x + -2x2 = 15 + -11x + 2x2 + -15 + 11x + -2x2

Combine like terms: -11 + -15 = -26
-26 + 4x + 11x + -2x2 = 15 + -11x + 2x2 + -15 + 11x + -2x2

Combine like terms: 4x + 11x = 15x
-26 + 15x + -2x2 = 15 + -11x + 2x2 + -15 + 11x + -2x2

Reorder the terms:
-26 + 15x + -2x2 = 15 + -15 + -11x + 11x + 2x2 + -2x2

Combine like terms: 15 + -15 = 0
-26 + 15x + -2x2 = 0 + -11x + 11x + 2x2 + -2x2
-26 + 15x + -2x2 = -11x + 11x + 2x2 + -2x2

Combine like terms: -11x + 11x = 0
-26 + 15x + -2x2 = 0 + 2x2 + -2x2
-26 + 15x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-26 + 15x + -2x2 = 0

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

Divide each side by '-2'.
13 + -7.5x + x2 = 0

Move the constant term to the right:

Add '-13' to each side of the equation.
13 + -7.5x + -13 + x2 = 0 + -13

Reorder the terms:
13 + -13 + -7.5x + x2 = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -7.5x + x2 = 0 + -13
-7.5x + x2 = 0 + -13

Combine like terms: 0 + -13 = -13
-7.5x + x2 = -13

The x term is -7.5x.  Take half its coefficient (-3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
-7.5x + 14.0625 + x2 = -13 + 14.0625

Reorder the terms:
14.0625 + -7.5x + x2 = -13 + 14.0625

Combine like terms: -13 + 14.0625 = 1.0625
14.0625 + -7.5x + x2 = 1.0625

Factor a perfect square on the left side:
(x + -3.75)(x + -3.75) = 1.0625

Calculate the square root of the right side: 1.030776406

Break this problem into two subproblems by setting 
(x + -3.75) equal to 1.030776406 and -1.030776406.

Subproblem 1

x + -3.75 = 1.030776406 Simplifying x + -3.75 = 1.030776406 Reorder the terms: -3.75 + x = 1.030776406 Solving -3.75 + x = 1.030776406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = 1.030776406 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = 1.030776406 + 3.75 x = 1.030776406 + 3.75 Combine like terms: 1.030776406 + 3.75 = 4.780776406 x = 4.780776406 Simplifying x = 4.780776406

Subproblem 2

x + -3.75 = -1.030776406 Simplifying x + -3.75 = -1.030776406 Reorder the terms: -3.75 + x = -1.030776406 Solving -3.75 + x = -1.030776406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = -1.030776406 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = -1.030776406 + 3.75 x = -1.030776406 + 3.75 Combine like terms: -1.030776406 + 3.75 = 2.719223594 x = 2.719223594 Simplifying x = 2.719223594

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.780776406, 2.719223594}

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