x^2+3x=90000

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Solution for x^2+3x=90000 equation:


Simplifying
x2 + 3x = 90000

Reorder the terms:
3x + x2 = 90000

Solving
3x + x2 = 90000

Solving for variable 'x'.

Reorder the terms:
-90000 + 3x + x2 = 90000 + -90000

Combine like terms: 90000 + -90000 = 0
-90000 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '90000' to each side of the equation.
-90000 + 3x + 90000 + x2 = 0 + 90000

Reorder the terms:
-90000 + 90000 + 3x + x2 = 0 + 90000

Combine like terms: -90000 + 90000 = 0
0 + 3x + x2 = 0 + 90000
3x + x2 = 0 + 90000

Combine like terms: 0 + 90000 = 90000
3x + x2 = 90000

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 90000 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 90000 + 2.25

Combine like terms: 90000 + 2.25 = 90002.25
2.25 + 3x + x2 = 90002.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 90002.25

Calculate the square root of the right side: 300.003749977

Break this problem into two subproblems by setting 
(x + 1.5) equal to 300.003749977 and -300.003749977.

Subproblem 1

x + 1.5 = 300.003749977 Simplifying x + 1.5 = 300.003749977 Reorder the terms: 1.5 + x = 300.003749977 Solving 1.5 + x = 300.003749977 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 300.003749977 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 300.003749977 + -1.5 x = 300.003749977 + -1.5 Combine like terms: 300.003749977 + -1.5 = 298.503749977 x = 298.503749977 Simplifying x = 298.503749977

Subproblem 2

x + 1.5 = -300.003749977 Simplifying x + 1.5 = -300.003749977 Reorder the terms: 1.5 + x = -300.003749977 Solving 1.5 + x = -300.003749977 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -300.003749977 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -300.003749977 + -1.5 x = -300.003749977 + -1.5 Combine like terms: -300.003749977 + -1.5 = -301.503749977 x = -301.503749977 Simplifying x = -301.503749977

Solution

The solution to the problem is based on the solutions from the subproblems. x = {298.503749977, -301.503749977}

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