x^2+10x=40

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Solution for x^2+10x=40 equation:


Simplifying
x2 + 10x = 40

Reorder the terms:
10x + x2 = 40

Solving
10x + x2 = 40

Solving for variable 'x'.

Reorder the terms:
-40 + 10x + x2 = 40 + -40

Combine like terms: 40 + -40 = 0
-40 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + 10x + 40 + x2 = 0 + 40

Reorder the terms:
-40 + 40 + 10x + x2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + 10x + x2 = 0 + 40
10x + x2 = 0 + 40

Combine like terms: 0 + 40 = 40
10x + x2 = 40

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 = 40 + 25

Reorder the terms:
25 + 10x + x2 = 40 + 25

Combine like terms: 40 + 25 = 65
25 + 10x + x2 = 65

Factor a perfect square on the left side:
(x + 5)(x + 5) = 65

Calculate the square root of the right side: 8.062257748

Break this problem into two subproblems by setting 
(x + 5) equal to 8.062257748 and -8.062257748.

Subproblem 1

x + 5 = 8.062257748 Simplifying x + 5 = 8.062257748 Reorder the terms: 5 + x = 8.062257748 Solving 5 + x = 8.062257748 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 = 8.062257748 + -5 Combine like terms: 5 + -5 = 0 0 + x = 8.062257748 + -5 x = 8.062257748 + -5 Combine like terms: 8.062257748 + -5 = 3.062257748 x = 3.062257748 Simplifying x = 3.062257748

Subproblem 2

x + 5 = -8.062257748 Simplifying x + 5 = -8.062257748 Reorder the terms: 5 + x = -8.062257748 Solving 5 + x = -8.062257748 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 = -8.062257748 + -5 Combine like terms: 5 + -5 = 0 0 + x = -8.062257748 + -5 x = -8.062257748 + -5 Combine like terms: -8.062257748 + -5 = -13.062257748 x = -13.062257748 Simplifying x = -13.062257748

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.062257748, -13.062257748}

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