140-43x-x^2=0

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Solution for 140-43x-x^2=0 equation:


Simplifying
140 + -43x + -1x2 = 0

Solving
140 + -43x + -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'.
-140 + 43x + x2 = 0

Move the constant term to the right:

Add '140' to each side of the equation.
-140 + 43x + 140 + x2 = 0 + 140

Reorder the terms:
-140 + 140 + 43x + x2 = 0 + 140

Combine like terms: -140 + 140 = 0
0 + 43x + x2 = 0 + 140
43x + x2 = 0 + 140

Combine like terms: 0 + 140 = 140
43x + x2 = 140

The x term is 43x.  Take half its coefficient (21.5).
Square it (462.25) and add it to both sides.

Add '462.25' to each side of the equation.
43x + 462.25 + x2 = 140 + 462.25

Reorder the terms:
462.25 + 43x + x2 = 140 + 462.25

Combine like terms: 140 + 462.25 = 602.25
462.25 + 43x + x2 = 602.25

Factor a perfect square on the left side:
(x + 21.5)(x + 21.5) = 602.25

Calculate the square root of the right side: 24.540782384

Break this problem into two subproblems by setting 
(x + 21.5) equal to 24.540782384 and -24.540782384.

Subproblem 1

x + 21.5 = 24.540782384 Simplifying x + 21.5 = 24.540782384 Reorder the terms: 21.5 + x = 24.540782384 Solving 21.5 + x = 24.540782384 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-21.5' to each side of the equation. 21.5 + -21.5 + x = 24.540782384 + -21.5 Combine like terms: 21.5 + -21.5 = 0.0 0.0 + x = 24.540782384 + -21.5 x = 24.540782384 + -21.5 Combine like terms: 24.540782384 + -21.5 = 3.040782384 x = 3.040782384 Simplifying x = 3.040782384

Subproblem 2

x + 21.5 = -24.540782384 Simplifying x + 21.5 = -24.540782384 Reorder the terms: 21.5 + x = -24.540782384 Solving 21.5 + x = -24.540782384 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-21.5' to each side of the equation. 21.5 + -21.5 + x = -24.540782384 + -21.5 Combine like terms: 21.5 + -21.5 = 0.0 0.0 + x = -24.540782384 + -21.5 x = -24.540782384 + -21.5 Combine like terms: -24.540782384 + -21.5 = -46.040782384 x = -46.040782384 Simplifying x = -46.040782384

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.040782384, -46.040782384}

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