2x^2+90x+1000=1288

Solution for 2x^2+90x+1000=1288 equation:

Simplifying
2x2 + 90x + 1000 = 1288

Reorder the terms:
1000 + 90x + 2x2 = 1288

Solving
1000 + 90x + 2x2 = 1288

Solving for variable 'x'.

Reorder the terms:
1000 + -1288 + 90x + 2x2 = 1288 + -1288

Combine like terms: 1000 + -1288 = -288
-288 + 90x + 2x2 = 1288 + -1288

Combine like terms: 1288 + -1288 = 0
-288 + 90x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-144 + 45x + x2) = 0

Factor a trinomial.
2((-48 + -1x)(3 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-48 + -1x)' equal to zero and attempt to solve:

Simplifying
-48 + -1x = 0

Solving
-48 + -1x = 0

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

Add '48' to each side of the equation.
-48 + 48 + -1x = 0 + 48

Combine like terms: -48 + 48 = 0
0 + -1x = 0 + 48
-1x = 0 + 48

Combine like terms: 0 + 48 = 48
-1x = 48

Divide each side by '-1'.
x = -48

Simplifying
x = -48
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-48, 3}