x^2+5x-59=0

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Solution for x^2+5x-59=0 equation:


Simplifying
x2 + 5x + -59 = 0

Reorder the terms:
-59 + 5x + x2 = 0

Solving
-59 + 5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '59' to each side of the equation.
-59 + 5x + 59 + x2 = 0 + 59

Reorder the terms:
-59 + 59 + 5x + x2 = 0 + 59

Combine like terms: -59 + 59 = 0
0 + 5x + x2 = 0 + 59
5x + x2 = 0 + 59

Combine like terms: 0 + 59 = 59
5x + x2 = 59

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 59 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 59 + 6.25

Combine like terms: 59 + 6.25 = 65.25
6.25 + 5x + x2 = 65.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 65.25

Calculate the square root of the right side: 8.077747211

Break this problem into two subproblems by setting 
(x + 2.5) equal to 8.077747211 and -8.077747211.

Subproblem 1

x + 2.5 = 8.077747211 Simplifying x + 2.5 = 8.077747211 Reorder the terms: 2.5 + x = 8.077747211 Solving 2.5 + x = 8.077747211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 8.077747211 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 8.077747211 + -2.5 x = 8.077747211 + -2.5 Combine like terms: 8.077747211 + -2.5 = 5.577747211 x = 5.577747211 Simplifying x = 5.577747211

Subproblem 2

x + 2.5 = -8.077747211 Simplifying x + 2.5 = -8.077747211 Reorder the terms: 2.5 + x = -8.077747211 Solving 2.5 + x = -8.077747211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -8.077747211 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -8.077747211 + -2.5 x = -8.077747211 + -2.5 Combine like terms: -8.077747211 + -2.5 = -10.577747211 x = -10.577747211 Simplifying x = -10.577747211

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.577747211, -10.577747211}

 

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