80=x^2+10x

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Solution for 80=x^2+10x equation:


Simplifying
80 = x2 + 10x

Reorder the terms:
80 = 10x + x2

Solving
80 = 10x + x2

Solving for variable 'x'.

Reorder the terms:
80 + -10x + -1x2 = 10x + -10x + x2 + -1x2

Combine like terms: 10x + -10x = 0
80 + -10x + -1x2 = 0 + x2 + -1x2
80 + -10x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
80 + -10x + -1x2 = 0

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

Divide each side by '-1'.
-80 + 10x + x2 = 0

Move the constant term to the right:

Add '80' to each side of the equation.
-80 + 10x + 80 + x2 = 0 + 80

Reorder the terms:
-80 + 80 + 10x + x2 = 0 + 80

Combine like terms: -80 + 80 = 0
0 + 10x + x2 = 0 + 80
10x + x2 = 0 + 80

Combine like terms: 0 + 80 = 80
10x + x2 = 80

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = 80 + 25

Reorder the terms:
25 + 10x + x2 = 80 + 25

Combine like terms: 80 + 25 = 105
25 + 10x + x2 = 105

Factor a perfect square on the left side:
(x + 5)(x + 5) = 105

Calculate the square root of the right side: 10.246950766

Break this problem into two subproblems by setting 
(x + 5) equal to 10.246950766 and -10.246950766.

Subproblem 1

x + 5 = 10.246950766 Simplifying x + 5 = 10.246950766 Reorder the terms: 5 + x = 10.246950766 Solving 5 + x = 10.246950766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 10.246950766 + -5 Combine like terms: 5 + -5 = 0 0 + x = 10.246950766 + -5 x = 10.246950766 + -5 Combine like terms: 10.246950766 + -5 = 5.246950766 x = 5.246950766 Simplifying x = 5.246950766

Subproblem 2

x + 5 = -10.246950766 Simplifying x + 5 = -10.246950766 Reorder the terms: 5 + x = -10.246950766 Solving 5 + x = -10.246950766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -10.246950766 + -5 Combine like terms: 5 + -5 = 0 0 + x = -10.246950766 + -5 x = -10.246950766 + -5 Combine like terms: -10.246950766 + -5 = -15.246950766 x = -15.246950766 Simplifying x = -15.246950766

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.246950766, -15.246950766}

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