x^2+3*x=1852

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Solution for x^2+3*x=1852 equation:


Simplifying
x2 + 3x = 1852

Reorder the terms:
3x + x2 = 1852

Solving
3x + x2 = 1852

Solving for variable 'x'.

Reorder the terms:
-1852 + 3x + x2 = 1852 + -1852

Combine like terms: 1852 + -1852 = 0
-1852 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1852' to each side of the equation.
-1852 + 3x + 1852 + x2 = 0 + 1852

Reorder the terms:
-1852 + 1852 + 3x + x2 = 0 + 1852

Combine like terms: -1852 + 1852 = 0
0 + 3x + x2 = 0 + 1852
3x + x2 = 0 + 1852

Combine like terms: 0 + 1852 = 1852
3x + x2 = 1852

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 = 1852 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 1852 + 2.25

Combine like terms: 1852 + 2.25 = 1854.25
2.25 + 3x + x2 = 1854.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 1854.25

Calculate the square root of the right side: 43.06100324

Break this problem into two subproblems by setting 
(x + 1.5) equal to 43.06100324 and -43.06100324.

Subproblem 1

x + 1.5 = 43.06100324 Simplifying x + 1.5 = 43.06100324 Reorder the terms: 1.5 + x = 43.06100324 Solving 1.5 + x = 43.06100324 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 = 43.06100324 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 43.06100324 + -1.5 x = 43.06100324 + -1.5 Combine like terms: 43.06100324 + -1.5 = 41.56100324 x = 41.56100324 Simplifying x = 41.56100324

Subproblem 2

x + 1.5 = -43.06100324 Simplifying x + 1.5 = -43.06100324 Reorder the terms: 1.5 + x = -43.06100324 Solving 1.5 + x = -43.06100324 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 = -43.06100324 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -43.06100324 + -1.5 x = -43.06100324 + -1.5 Combine like terms: -43.06100324 + -1.5 = -44.56100324 x = -44.56100324 Simplifying x = -44.56100324

Solution

The solution to the problem is based on the solutions from the subproblems. x = {41.56100324, -44.56100324}

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