1200+x-x^2=0

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Solution for 1200+x-x^2=0 equation:


Simplifying
1200 + x + -1x2 = 0

Solving
1200 + x + -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'.
-1200 + -1x + x2 = 0

Move the constant term to the right:

Add '1200' to each side of the equation.
-1200 + -1x + 1200 + x2 = 0 + 1200

Reorder the terms:
-1200 + 1200 + -1x + x2 = 0 + 1200

Combine like terms: -1200 + 1200 = 0
0 + -1x + x2 = 0 + 1200
-1x + x2 = 0 + 1200

Combine like terms: 0 + 1200 = 1200
-1x + x2 = 1200

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 1200 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 1200 + 0.25

Combine like terms: 1200 + 0.25 = 1200.25
0.25 + -1x + x2 = 1200.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 1200.25

Calculate the square root of the right side: 34.644624403

Break this problem into two subproblems by setting 
(x + 0.5) equal to 34.644624403 and -34.644624403.

Subproblem 1

x + 0.5 = 34.644624403 Simplifying x + 0.5 = 34.644624403 Reorder the terms: 0.5 + x = 34.644624403 Solving 0.5 + x = 34.644624403 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 34.644624403 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 34.644624403 + -0.5 x = 34.644624403 + -0.5 Combine like terms: 34.644624403 + -0.5 = 34.144624403 x = 34.144624403 Simplifying x = 34.144624403

Subproblem 2

x + 0.5 = -34.644624403 Simplifying x + 0.5 = -34.644624403 Reorder the terms: 0.5 + x = -34.644624403 Solving 0.5 + x = -34.644624403 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -34.644624403 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -34.644624403 + -0.5 x = -34.644624403 + -0.5 Combine like terms: -34.644624403 + -0.5 = -35.144624403 x = -35.144624403 Simplifying x = -35.144624403

Solution

The solution to the problem is based on the solutions from the subproblems. x = {34.144624403, -35.144624403}

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