5x^2+25=36x+36

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Solution for 5x^2+25=36x+36 equation:


Simplifying
5x2 + 25 = 36x + 36

Reorder the terms:
25 + 5x2 = 36x + 36

Reorder the terms:
25 + 5x2 = 36 + 36x

Solving
25 + 5x2 = 36 + 36x

Solving for variable 'x'.

Reorder the terms:
25 + -36 + -36x + 5x2 = 36 + 36x + -36 + -36x

Combine like terms: 25 + -36 = -11
-11 + -36x + 5x2 = 36 + 36x + -36 + -36x

Reorder the terms:
-11 + -36x + 5x2 = 36 + -36 + 36x + -36x

Combine like terms: 36 + -36 = 0
-11 + -36x + 5x2 = 0 + 36x + -36x
-11 + -36x + 5x2 = 36x + -36x

Combine like terms: 36x + -36x = 0
-11 + -36x + 5x2 = 0

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

Divide each side by '5'.
-2.2 + -7.2x + x2 = 0

Move the constant term to the right:

Add '2.2' to each side of the equation.
-2.2 + -7.2x + 2.2 + x2 = 0 + 2.2

Reorder the terms:
-2.2 + 2.2 + -7.2x + x2 = 0 + 2.2

Combine like terms: -2.2 + 2.2 = 0.0
0.0 + -7.2x + x2 = 0 + 2.2
-7.2x + x2 = 0 + 2.2

Combine like terms: 0 + 2.2 = 2.2
-7.2x + x2 = 2.2

The x term is -7.2x.  Take half its coefficient (-3.6).
Square it (12.96) and add it to both sides.

Add '12.96' to each side of the equation.
-7.2x + 12.96 + x2 = 2.2 + 12.96

Reorder the terms:
12.96 + -7.2x + x2 = 2.2 + 12.96

Combine like terms: 2.2 + 12.96 = 15.16
12.96 + -7.2x + x2 = 15.16

Factor a perfect square on the left side:
(x + -3.6)(x + -3.6) = 15.16

Calculate the square root of the right side: 3.893584467

Break this problem into two subproblems by setting 
(x + -3.6) equal to 3.893584467 and -3.893584467.

Subproblem 1

x + -3.6 = 3.893584467 Simplifying x + -3.6 = 3.893584467 Reorder the terms: -3.6 + x = 3.893584467 Solving -3.6 + x = 3.893584467 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.6' to each side of the equation. -3.6 + 3.6 + x = 3.893584467 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + x = 3.893584467 + 3.6 x = 3.893584467 + 3.6 Combine like terms: 3.893584467 + 3.6 = 7.493584467 x = 7.493584467 Simplifying x = 7.493584467

Subproblem 2

x + -3.6 = -3.893584467 Simplifying x + -3.6 = -3.893584467 Reorder the terms: -3.6 + x = -3.893584467 Solving -3.6 + x = -3.893584467 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.6' to each side of the equation. -3.6 + 3.6 + x = -3.893584467 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + x = -3.893584467 + 3.6 x = -3.893584467 + 3.6 Combine like terms: -3.893584467 + 3.6 = -0.293584467 x = -0.293584467 Simplifying x = -0.293584467

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.493584467, -0.293584467}

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