121=x^2+5x

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Solution for 121=x^2+5x equation:


Simplifying
121 = x2 + 5x

Reorder the terms:
121 = 5x + x2

Solving
121 = 5x + x2

Solving for variable 'x'.

Reorder the terms:
121 + -5x + -1x2 = 5x + -5x + x2 + -1x2

Combine like terms: 5x + -5x = 0
121 + -5x + -1x2 = 0 + x2 + -1x2
121 + -5x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
121 + -5x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-121 + 5x + x2 = 0

Move the constant term to the right:

Add '121' to each side of the equation.
-121 + 5x + 121 + x2 = 0 + 121

Reorder the terms:
-121 + 121 + 5x + x2 = 0 + 121

Combine like terms: -121 + 121 = 0
0 + 5x + x2 = 0 + 121
5x + x2 = 0 + 121

Combine like terms: 0 + 121 = 121
5x + x2 = 121

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 121 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 121 + 6.25

Combine like terms: 121 + 6.25 = 127.25
6.25 + 5x + x2 = 127.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 127.25

Calculate the square root of the right side: 11.280514173

Break this problem into two subproblems by setting 
(x + 2.5) equal to 11.280514173 and -11.280514173.

Subproblem 1

x + 2.5 = 11.280514173 Simplifying x + 2.5 = 11.280514173 Reorder the terms: 2.5 + x = 11.280514173 Solving 2.5 + x = 11.280514173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 11.280514173 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 11.280514173 + -2.5 x = 11.280514173 + -2.5 Combine like terms: 11.280514173 + -2.5 = 8.780514173 x = 8.780514173 Simplifying x = 8.780514173

Subproblem 2

x + 2.5 = -11.280514173 Simplifying x + 2.5 = -11.280514173 Reorder the terms: 2.5 + x = -11.280514173 Solving 2.5 + x = -11.280514173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -11.280514173 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -11.280514173 + -2.5 x = -11.280514173 + -2.5 Combine like terms: -11.280514173 + -2.5 = -13.780514173 x = -13.780514173 Simplifying x = -13.780514173

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.780514173, -13.780514173}

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