x^2+3x=11

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Solution for x^2+3x=11 equation:


Simplifying
x2 + 3x = 11

Reorder the terms:
3x + x2 = 11

Solving
3x + x2 = 11

Solving for variable 'x'.

Reorder the terms:
-11 + 3x + x2 = 11 + -11

Combine like terms: 11 + -11 = 0
-11 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + 3x + 11 + x2 = 0 + 11

Reorder the terms:
-11 + 11 + 3x + x2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + 3x + x2 = 0 + 11
3x + x2 = 0 + 11

Combine like terms: 0 + 11 = 11
3x + x2 = 11

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 = 11 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 11 + 2.25

Combine like terms: 11 + 2.25 = 13.25
2.25 + 3x + x2 = 13.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 13.25

Calculate the square root of the right side: 3.640054945

Break this problem into two subproblems by setting 
(x + 1.5) equal to 3.640054945 and -3.640054945.

Subproblem 1

x + 1.5 = 3.640054945 Simplifying x + 1.5 = 3.640054945 Reorder the terms: 1.5 + x = 3.640054945 Solving 1.5 + x = 3.640054945 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 = 3.640054945 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 3.640054945 + -1.5 x = 3.640054945 + -1.5 Combine like terms: 3.640054945 + -1.5 = 2.140054945 x = 2.140054945 Simplifying x = 2.140054945

Subproblem 2

x + 1.5 = -3.640054945 Simplifying x + 1.5 = -3.640054945 Reorder the terms: 1.5 + x = -3.640054945 Solving 1.5 + x = -3.640054945 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 = -3.640054945 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -3.640054945 + -1.5 x = -3.640054945 + -1.5 Combine like terms: -3.640054945 + -1.5 = -5.140054945 x = -5.140054945 Simplifying x = -5.140054945

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.140054945, -5.140054945}

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