3x+x^2=225

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Solution for 3x+x^2=225 equation:


Simplifying
3x + x2 = 225

Solving
3x + x2 = 225

Solving for variable 'x'.

Reorder the terms:
-225 + 3x + x2 = 225 + -225

Combine like terms: 225 + -225 = 0
-225 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '225' to each side of the equation.
-225 + 3x + 225 + x2 = 0 + 225

Reorder the terms:
-225 + 225 + 3x + x2 = 0 + 225

Combine like terms: -225 + 225 = 0
0 + 3x + x2 = 0 + 225
3x + x2 = 0 + 225

Combine like terms: 0 + 225 = 225
3x + x2 = 225

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 = 225 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 225 + 2.25

Combine like terms: 225 + 2.25 = 227.25
2.25 + 3x + x2 = 227.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 227.25

Calculate the square root of the right side: 15.074813432

Break this problem into two subproblems by setting 
(x + 1.5) equal to 15.074813432 and -15.074813432.

Subproblem 1

x + 1.5 = 15.074813432 Simplifying x + 1.5 = 15.074813432 Reorder the terms: 1.5 + x = 15.074813432 Solving 1.5 + x = 15.074813432 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 = 15.074813432 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 15.074813432 + -1.5 x = 15.074813432 + -1.5 Combine like terms: 15.074813432 + -1.5 = 13.574813432 x = 13.574813432 Simplifying x = 13.574813432

Subproblem 2

x + 1.5 = -15.074813432 Simplifying x + 1.5 = -15.074813432 Reorder the terms: 1.5 + x = -15.074813432 Solving 1.5 + x = -15.074813432 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 = -15.074813432 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -15.074813432 + -1.5 x = -15.074813432 + -1.5 Combine like terms: -15.074813432 + -1.5 = -16.574813432 x = -16.574813432 Simplifying x = -16.574813432

Solution

The solution to the problem is based on the solutions from the subproblems. x = {13.574813432, -16.574813432}

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