x^2+10x-1600=0

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Solution for x^2+10x-1600=0 equation:


Simplifying
x2 + 10x + -1600 = 0

Reorder the terms:
-1600 + 10x + x2 = 0

Solving
-1600 + 10x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1600' to each side of the equation.
-1600 + 10x + 1600 + x2 = 0 + 1600

Reorder the terms:
-1600 + 1600 + 10x + x2 = 0 + 1600

Combine like terms: -1600 + 1600 = 0
0 + 10x + x2 = 0 + 1600
10x + x2 = 0 + 1600

Combine like terms: 0 + 1600 = 1600
10x + x2 = 1600

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 = 1600 + 25

Reorder the terms:
25 + 10x + x2 = 1600 + 25

Combine like terms: 1600 + 25 = 1625
25 + 10x + x2 = 1625

Factor a perfect square on the left side:
(x + 5)(x + 5) = 1625

Calculate the square root of the right side: 40.311288741

Break this problem into two subproblems by setting 
(x + 5) equal to 40.311288741 and -40.311288741.

Subproblem 1

x + 5 = 40.311288741 Simplifying x + 5 = 40.311288741 Reorder the terms: 5 + x = 40.311288741 Solving 5 + x = 40.311288741 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 = 40.311288741 + -5 Combine like terms: 5 + -5 = 0 0 + x = 40.311288741 + -5 x = 40.311288741 + -5 Combine like terms: 40.311288741 + -5 = 35.311288741 x = 35.311288741 Simplifying x = 35.311288741

Subproblem 2

x + 5 = -40.311288741 Simplifying x + 5 = -40.311288741 Reorder the terms: 5 + x = -40.311288741 Solving 5 + x = -40.311288741 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 = -40.311288741 + -5 Combine like terms: 5 + -5 = 0 0 + x = -40.311288741 + -5 x = -40.311288741 + -5 Combine like terms: -40.311288741 + -5 = -45.311288741 x = -45.311288741 Simplifying x = -45.311288741

Solution

The solution to the problem is based on the solutions from the subproblems. x = {35.311288741, -45.311288741}

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