x(x+34)=35

Solution for x(x+34)=35 equation:

Simplifying
x(x + 34) = 35

Reorder the terms:
x(34 + x) = 35
(34 * x + x * x) = 35
(34x + x2) = 35

Solving
34x + x2 = 35

Solving for variable 'x'.

Reorder the terms:
-35 + 34x + x2 = 35 + -35

Combine like terms: 35 + -35 = 0
-35 + 34x + x2 = 0

Factor a trinomial.
(-35 + -1x)(1 + -1x) = 0

Subproblem 1
Set the factor '(-35 + -1x)' equal to zero and attempt to solve:

Simplifying
-35 + -1x = 0

Solving
-35 + -1x = 0

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

Add '35' to each side of the equation.
-35 + 35 + -1x = 0 + 35

Combine like terms: -35 + 35 = 0
0 + -1x = 0 + 35
-1x = 0 + 35

Combine like terms: 0 + 35 = 35
-1x = 35

Divide each side by '-1'.
x = -35

Simplifying
x = -35
Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {-35, 1}