300-35x-x^2=0

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Solution for 300-35x-x^2=0 equation:


Simplifying
300 + -35x + -1x2 = 0

Solving
300 + -35x + -1x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-300 + 35x + x2 = 0

Move the constant term to the right:

Add '300' to each side of the equation.
-300 + 35x + 300 + x2 = 0 + 300

Reorder the terms:
-300 + 300 + 35x + x2 = 0 + 300

Combine like terms: -300 + 300 = 0
0 + 35x + x2 = 0 + 300
35x + x2 = 0 + 300

Combine like terms: 0 + 300 = 300
35x + x2 = 300

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 = 300 + 306.25

Reorder the terms:
306.25 + 35x + x2 = 300 + 306.25

Combine like terms: 300 + 306.25 = 606.25
306.25 + 35x + x2 = 606.25

Factor a perfect square on the left side:
(x + 17.5)(x + 17.5) = 606.25

Calculate the square root of the right side: 24.622144504

Break this problem into two subproblems by setting 
(x + 17.5) equal to 24.622144504 and -24.622144504.

Subproblem 1

x + 17.5 = 24.622144504 Simplifying x + 17.5 = 24.622144504 Reorder the terms: 17.5 + x = 24.622144504 Solving 17.5 + x = 24.622144504 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 = 24.622144504 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = 24.622144504 + -17.5 x = 24.622144504 + -17.5 Combine like terms: 24.622144504 + -17.5 = 7.122144504 x = 7.122144504 Simplifying x = 7.122144504

Subproblem 2

x + 17.5 = -24.622144504 Simplifying x + 17.5 = -24.622144504 Reorder the terms: 17.5 + x = -24.622144504 Solving 17.5 + x = -24.622144504 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 = -24.622144504 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = -24.622144504 + -17.5 x = -24.622144504 + -17.5 Combine like terms: -24.622144504 + -17.5 = -42.122144504 x = -42.122144504 Simplifying x = -42.122144504

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.122144504, -42.122144504}

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