3x^2+253x=180000

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Solution for 3x^2+253x=180000 equation:


Simplifying
3x2 + 253x = 180000

Reorder the terms:
253x + 3x2 = 180000

Solving
253x + 3x2 = 180000

Solving for variable 'x'.

Reorder the terms:
-180000 + 253x + 3x2 = 180000 + -180000

Combine like terms: 180000 + -180000 = 0
-180000 + 253x + 3x2 = 0

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

Divide each side by '3'.
-60000 + 84.33333333x + x2 = 0

Move the constant term to the right:

Add '60000' to each side of the equation.
-60000 + 84.33333333x + 60000 + x2 = 0 + 60000

Reorder the terms:
-60000 + 60000 + 84.33333333x + x2 = 0 + 60000

Combine like terms: -60000 + 60000 = 0
0 + 84.33333333x + x2 = 0 + 60000
84.33333333x + x2 = 0 + 60000

Combine like terms: 0 + 60000 = 60000
84.33333333x + x2 = 60000

The x term is 84.33333333x.  Take half its coefficient (42.16666667).
Square it (1778.027778) and add it to both sides.

Add '1778.027778' to each side of the equation.
84.33333333x + 1778.027778 + x2 = 60000 + 1778.027778

Reorder the terms:
1778.027778 + 84.33333333x + x2 = 60000 + 1778.027778

Combine like terms: 60000 + 1778.027778 = 61778.027778
1778.027778 + 84.33333333x + x2 = 61778.027778

Factor a perfect square on the left side:
(x + 42.16666667)(x + 42.16666667) = 61778.027778

Calculate the square root of the right side: 248.551861345

Break this problem into two subproblems by setting 
(x + 42.16666667) equal to 248.551861345 and -248.551861345.

Subproblem 1

x + 42.16666667 = 248.551861345 Simplifying x + 42.16666667 = 248.551861345 Reorder the terms: 42.16666667 + x = 248.551861345 Solving 42.16666667 + x = 248.551861345 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-42.16666667' to each side of the equation. 42.16666667 + -42.16666667 + x = 248.551861345 + -42.16666667 Combine like terms: 42.16666667 + -42.16666667 = 0.00000000 0.00000000 + x = 248.551861345 + -42.16666667 x = 248.551861345 + -42.16666667 Combine like terms: 248.551861345 + -42.16666667 = 206.385194675 x = 206.385194675 Simplifying x = 206.385194675

Subproblem 2

x + 42.16666667 = -248.551861345 Simplifying x + 42.16666667 = -248.551861345 Reorder the terms: 42.16666667 + x = -248.551861345 Solving 42.16666667 + x = -248.551861345 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-42.16666667' to each side of the equation. 42.16666667 + -42.16666667 + x = -248.551861345 + -42.16666667 Combine like terms: 42.16666667 + -42.16666667 = 0.00000000 0.00000000 + x = -248.551861345 + -42.16666667 x = -248.551861345 + -42.16666667 Combine like terms: -248.551861345 + -42.16666667 = -290.718528015 x = -290.718528015 Simplifying x = -290.718528015

Solution

The solution to the problem is based on the solutions from the subproblems. x = {206.385194675, -290.718528015}

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