(2x-5)(2x-5)-4x-10(x+3)=0

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Solution for (2x-5)(2x-5)-4x-10(x+3)=0 equation:


Simplifying
(2x + -5)(2x + -5) + -4x + -10(x + 3) = 0

Reorder the terms:
(-5 + 2x)(2x + -5) + -4x + -10(x + 3) = 0

Reorder the terms:
(-5 + 2x)(-5 + 2x) + -4x + -10(x + 3) = 0

Multiply (-5 + 2x) * (-5 + 2x)
(-5(-5 + 2x) + 2x * (-5 + 2x)) + -4x + -10(x + 3) = 0
((-5 * -5 + 2x * -5) + 2x * (-5 + 2x)) + -4x + -10(x + 3) = 0
((25 + -10x) + 2x * (-5 + 2x)) + -4x + -10(x + 3) = 0
(25 + -10x + (-5 * 2x + 2x * 2x)) + -4x + -10(x + 3) = 0
(25 + -10x + (-10x + 4x2)) + -4x + -10(x + 3) = 0

Combine like terms: -10x + -10x = -20x
(25 + -20x + 4x2) + -4x + -10(x + 3) = 0

Reorder the terms:
25 + -20x + 4x2 + -4x + -10(3 + x) = 0
25 + -20x + 4x2 + -4x + (3 * -10 + x * -10) = 0
25 + -20x + 4x2 + -4x + (-30 + -10x) = 0

Reorder the terms:
25 + -30 + -20x + -4x + -10x + 4x2 = 0

Combine like terms: 25 + -30 = -5
-5 + -20x + -4x + -10x + 4x2 = 0

Combine like terms: -20x + -4x = -24x
-5 + -24x + -10x + 4x2 = 0

Combine like terms: -24x + -10x = -34x
-5 + -34x + 4x2 = 0

Solving
-5 + -34x + 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'.
-1.25 + -8.5x + x2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + -8.5x + 1.25 + x2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + -8.5x + x2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + -8.5x + x2 = 0 + 1.25
-8.5x + x2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
-8.5x + x2 = 1.25

The x term is -8.5x.  Take half its coefficient (-4.25).
Square it (18.0625) and add it to both sides.

Add '18.0625' to each side of the equation.
-8.5x + 18.0625 + x2 = 1.25 + 18.0625

Reorder the terms:
18.0625 + -8.5x + x2 = 1.25 + 18.0625

Combine like terms: 1.25 + 18.0625 = 19.3125
18.0625 + -8.5x + x2 = 19.3125

Factor a perfect square on the left side:
(x + -4.25)(x + -4.25) = 19.3125

Calculate the square root of the right side: 4.394598958

Break this problem into two subproblems by setting 
(x + -4.25) equal to 4.394598958 and -4.394598958.

Subproblem 1

x + -4.25 = 4.394598958 Simplifying x + -4.25 = 4.394598958 Reorder the terms: -4.25 + x = 4.394598958 Solving -4.25 + x = 4.394598958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + x = 4.394598958 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = 4.394598958 + 4.25 x = 4.394598958 + 4.25 Combine like terms: 4.394598958 + 4.25 = 8.644598958 x = 8.644598958 Simplifying x = 8.644598958

Subproblem 2

x + -4.25 = -4.394598958 Simplifying x + -4.25 = -4.394598958 Reorder the terms: -4.25 + x = -4.394598958 Solving -4.25 + x = -4.394598958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + x = -4.394598958 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = -4.394598958 + 4.25 x = -4.394598958 + 4.25 Combine like terms: -4.394598958 + 4.25 = -0.144598958 x = -0.144598958 Simplifying x = -0.144598958

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.644598958, -0.144598958}

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