1000=-2x^2+70x+520

Solution for 1000=-2x^2+70x+520 equation:

Simplifying
1000 = -2x2 + 70x + 520

Reorder the terms:
1000 = 520 + 70x + -2x2

Solving
1000 = 520 + 70x + -2x2

Solving for variable 'x'.

Combine like terms: 1000 + -520 = 480
480 + -70x + 2x2 = 520 + 70x + -2x2 + -520 + -70x + 2x2

Reorder the terms:
480 + -70x + 2x2 = 520 + -520 + 70x + -70x + -2x2 + 2x2

Combine like terms: 520 + -520 = 0
480 + -70x + 2x2 = 0 + 70x + -70x + -2x2 + 2x2
480 + -70x + 2x2 = 70x + -70x + -2x2 + 2x2

Combine like terms: 70x + -70x = 0
480 + -70x + 2x2 = 0 + -2x2 + 2x2
480 + -70x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
480 + -70x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(240 + -35x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(240 + -35x + x2)' equal to zero and attempt to solve:

Simplifying
240 + -35x + x2 = 0

Solving
240 + -35x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-240' to each side of the equation.
240 + -35x + -240 + x2 = 0 + -240

Reorder the terms:
240 + -240 + -35x + x2 = 0 + -240

Combine like terms: 240 + -240 = 0
0 + -35x + x2 = 0 + -240
-35x + x2 = 0 + -240

Combine like terms: 0 + -240 = -240
-35x + x2 = -240

The x term is -35x.  Take half its coefficient (-17.5).
Square it (306.25) and add it to both sides.

Add '306.25' to each side of the equation.
-35x + 306.25 + x2 = -240 + 306.25

Reorder the terms:
306.25 + -35x + x2 = -240 + 306.25

Combine like terms: -240 + 306.25 = 66.25
306.25 + -35x + x2 = 66.25

Factor a perfect square on the left side:
(x + -17.5)(x + -17.5) = 66.25

Calculate the square root of the right side: 8.139410298

Break this problem into two subproblems by setting 
(x + -17.5) equal to 8.139410298 and -8.139410298.

Subproblem 1
x + -17.5 = 8.139410298

Simplifying
x + -17.5 = 8.139410298

Reorder the terms:
-17.5 + x = 8.139410298

Solving
-17.5 + x = 8.139410298

Solving for variable 'x'.

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

Add '17.5' to each side of the equation.
-17.5 + 17.5 + x = 8.139410298 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + x = 8.139410298 + 17.5
x = 8.139410298 + 17.5

Combine like terms: 8.139410298 + 17.5 = 25.639410298
x = 25.639410298

Simplifying
x = 25.639410298

Subproblem 2
x + -17.5 = -8.139410298

Simplifying
x + -17.5 = -8.139410298

Reorder the terms:
-17.5 + x = -8.139410298

Solving
-17.5 + x = -8.139410298

Solving for variable 'x'.

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

Add '17.5' to each side of the equation.
-17.5 + 17.5 + x = -8.139410298 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + x = -8.139410298 + 17.5
x = -8.139410298 + 17.5

Combine like terms: -8.139410298 + 17.5 = 9.360589702
x = 9.360589702

Simplifying
x = 9.360589702

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {25.639410298, 9.360589702}
Solution
x = {25.639410298, 9.360589702}