x^2+3x-13=0

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Solution for x^2+3x-13=0 equation:


Simplifying
x2 + 3x + -13 = 0

Reorder the terms:
-13 + 3x + x2 = 0

Solving
-13 + 3x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '13' to each side of the equation.
-13 + 3x + 13 + x2 = 0 + 13

Reorder the terms:
-13 + 13 + 3x + x2 = 0 + 13

Combine like terms: -13 + 13 = 0
0 + 3x + x2 = 0 + 13
3x + x2 = 0 + 13

Combine like terms: 0 + 13 = 13
3x + x2 = 13

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 = 13 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 13 + 2.25

Combine like terms: 13 + 2.25 = 15.25
2.25 + 3x + x2 = 15.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 15.25

Calculate the square root of the right side: 3.905124838

Break this problem into two subproblems by setting 
(x + 1.5) equal to 3.905124838 and -3.905124838.

Subproblem 1

x + 1.5 = 3.905124838 Simplifying x + 1.5 = 3.905124838 Reorder the terms: 1.5 + x = 3.905124838 Solving 1.5 + x = 3.905124838 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 = 3.905124838 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 3.905124838 + -1.5 x = 3.905124838 + -1.5 Combine like terms: 3.905124838 + -1.5 = 2.405124838 x = 2.405124838 Simplifying x = 2.405124838

Subproblem 2

x + 1.5 = -3.905124838 Simplifying x + 1.5 = -3.905124838 Reorder the terms: 1.5 + x = -3.905124838 Solving 1.5 + x = -3.905124838 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 = -3.905124838 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -3.905124838 + -1.5 x = -3.905124838 + -1.5 Combine like terms: -3.905124838 + -1.5 = -5.405124838 x = -5.405124838 Simplifying x = -5.405124838

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.405124838, -5.405124838}

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