8x^2+36x+36=25

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Solution for 8x^2+36x+36=25 equation:


Simplifying
8x2 + 36x + 36 = 25

Reorder the terms:
36 + 36x + 8x2 = 25

Solving
36 + 36x + 8x2 = 25

Solving for variable 'x'.

Reorder the terms:
36 + -25 + 36x + 8x2 = 25 + -25

Combine like terms: 36 + -25 = 11
11 + 36x + 8x2 = 25 + -25

Combine like terms: 25 + -25 = 0
11 + 36x + 8x2 = 0

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

Divide each side by '8'.
1.375 + 4.5x + x2 = 0

Move the constant term to the right:

Add '-1.375' to each side of the equation.
1.375 + 4.5x + -1.375 + x2 = 0 + -1.375

Reorder the terms:
1.375 + -1.375 + 4.5x + x2 = 0 + -1.375

Combine like terms: 1.375 + -1.375 = 0.000
0.000 + 4.5x + x2 = 0 + -1.375
4.5x + x2 = 0 + -1.375

Combine like terms: 0 + -1.375 = -1.375
4.5x + x2 = -1.375

The x term is 4.5x.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5x + 5.0625 + x2 = -1.375 + 5.0625

Reorder the terms:
5.0625 + 4.5x + x2 = -1.375 + 5.0625

Combine like terms: -1.375 + 5.0625 = 3.6875
5.0625 + 4.5x + x2 = 3.6875

Factor a perfect square on the left side:
(x + 2.25)(x + 2.25) = 3.6875

Calculate the square root of the right side: 1.920286437

Break this problem into two subproblems by setting 
(x + 2.25) equal to 1.920286437 and -1.920286437.

Subproblem 1

x + 2.25 = 1.920286437 Simplifying x + 2.25 = 1.920286437 Reorder the terms: 2.25 + x = 1.920286437 Solving 2.25 + x = 1.920286437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 1.920286437 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 1.920286437 + -2.25 x = 1.920286437 + -2.25 Combine like terms: 1.920286437 + -2.25 = -0.329713563 x = -0.329713563 Simplifying x = -0.329713563

Subproblem 2

x + 2.25 = -1.920286437 Simplifying x + 2.25 = -1.920286437 Reorder the terms: 2.25 + x = -1.920286437 Solving 2.25 + x = -1.920286437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -1.920286437 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -1.920286437 + -2.25 x = -1.920286437 + -2.25 Combine like terms: -1.920286437 + -2.25 = -4.170286437 x = -4.170286437 Simplifying x = -4.170286437

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.329713563, -4.170286437}

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