4X(X+5)-11=4X+17X+4

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Solution for 4X(X+5)-11=4X+17X+4 equation:


Simplifying
4X(X + 5) + -11 = 4X + 17X + 4

Reorder the terms:
4X(5 + X) + -11 = 4X + 17X + 4
(5 * 4X + X * 4X) + -11 = 4X + 17X + 4
(20X + 4X2) + -11 = 4X + 17X + 4

Reorder the terms:
-11 + 20X + 4X2 = 4X + 17X + 4

Reorder the terms:
-11 + 20X + 4X2 = 4 + 4X + 17X

Combine like terms: 4X + 17X = 21X
-11 + 20X + 4X2 = 4 + 21X

Solving
-11 + 20X + 4X2 = 4 + 21X

Solving for variable 'X'.

Reorder the terms:
-11 + -4 + 20X + -21X + 4X2 = 4 + 21X + -4 + -21X

Combine like terms: -11 + -4 = -15
-15 + 20X + -21X + 4X2 = 4 + 21X + -4 + -21X

Combine like terms: 20X + -21X = -1X
-15 + -1X + 4X2 = 4 + 21X + -4 + -21X

Reorder the terms:
-15 + -1X + 4X2 = 4 + -4 + 21X + -21X

Combine like terms: 4 + -4 = 0
-15 + -1X + 4X2 = 0 + 21X + -21X
-15 + -1X + 4X2 = 21X + -21X

Combine like terms: 21X + -21X = 0
-15 + -1X + 4X2 = 0

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

Divide each side by '4'.
-3.75 + -0.25X + X2 = 0

Move the constant term to the right:

Add '3.75' to each side of the equation.
-3.75 + -0.25X + 3.75 + X2 = 0 + 3.75

Reorder the terms:
-3.75 + 3.75 + -0.25X + X2 = 0 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + -0.25X + X2 = 0 + 3.75
-0.25X + X2 = 0 + 3.75

Combine like terms: 0 + 3.75 = 3.75
-0.25X + X2 = 3.75

The X term is -0.25X.  Take half its coefficient (-0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
-0.25X + 0.015625 + X2 = 3.75 + 0.015625

Reorder the terms:
0.015625 + -0.25X + X2 = 3.75 + 0.015625

Combine like terms: 3.75 + 0.015625 = 3.765625
0.015625 + -0.25X + X2 = 3.765625

Factor a perfect square on the left side:
(X + -0.125)(X + -0.125) = 3.765625

Calculate the square root of the right side: 1.940521837

Break this problem into two subproblems by setting 
(X + -0.125) equal to 1.940521837 and -1.940521837.

Subproblem 1

X + -0.125 = 1.940521837 Simplifying X + -0.125 = 1.940521837 Reorder the terms: -0.125 + X = 1.940521837 Solving -0.125 + X = 1.940521837 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + X = 1.940521837 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + X = 1.940521837 + 0.125 X = 1.940521837 + 0.125 Combine like terms: 1.940521837 + 0.125 = 2.065521837 X = 2.065521837 Simplifying X = 2.065521837

Subproblem 2

X + -0.125 = -1.940521837 Simplifying X + -0.125 = -1.940521837 Reorder the terms: -0.125 + X = -1.940521837 Solving -0.125 + X = -1.940521837 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + X = -1.940521837 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + X = -1.940521837 + 0.125 X = -1.940521837 + 0.125 Combine like terms: -1.940521837 + 0.125 = -1.815521837 X = -1.815521837 Simplifying X = -1.815521837

Solution

The solution to the problem is based on the solutions from the subproblems. X = {2.065521837, -1.815521837}

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