x(34+x)=71000

Solution for x(34+x)=71000 equation:

Simplifying
x(34 + x) = 71000
(34 * x + x * x) = 71000
(34x + x2) = 71000

Solving
34x + x2 = 71000

Solving for variable 'x'.

Reorder the terms:
-71000 + 34x + x2 = 71000 + -71000

Combine like terms: 71000 + -71000 = 0
-71000 + 34x + x2 = 0

Factor a trinomial.
(-284 + -1x)(250 + -1x) = 0

Subproblem 1
Set the factor '(-284 + -1x)' equal to zero and attempt to solve:

Simplifying
-284 + -1x = 0

Solving
-284 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '284' to each side of the equation.
-284 + 284 + -1x = 0 + 284

Combine like terms: -284 + 284 = 0
0 + -1x = 0 + 284
-1x = 0 + 284

Combine like terms: 0 + 284 = 284
-1x = 284

Divide each side by '-1'.
x = -284

Simplifying
x = -284
Subproblem 2
Set the factor '(250 + -1x)' equal to zero and attempt to solve:

Simplifying
250 + -1x = 0

Solving
250 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-250' to each side of the equation.
250 + -250 + -1x = 0 + -250

Combine like terms: 250 + -250 = 0
0 + -1x = 0 + -250
-1x = 0 + -250

Combine like terms: 0 + -250 = -250
-1x = -250

Divide each side by '-1'.
x = 250

Simplifying
x = 250
Solution
x = {-284, 250}