x^2+29x-6=0

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Solution for x^2+29x-6=0 equation:


Simplifying
x2 + 29x + -6 = 0

Reorder the terms:
-6 + 29x + x2 = 0

Solving
-6 + 29x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 29x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + 29x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 29x + x2 = 0 + 6
29x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
29x + x2 = 6

The x term is 29x.  Take half its coefficient (14.5).
Square it (210.25) and add it to both sides.

Add '210.25' to each side of the equation.
29x + 210.25 + x2 = 6 + 210.25

Reorder the terms:
210.25 + 29x + x2 = 6 + 210.25

Combine like terms: 6 + 210.25 = 216.25
210.25 + 29x + x2 = 216.25

Factor a perfect square on the left side:
(x + 14.5)(x + 14.5) = 216.25

Calculate the square root of the right side: 14.70544117

Break this problem into two subproblems by setting 
(x + 14.5) equal to 14.70544117 and -14.70544117.

Subproblem 1

x + 14.5 = 14.70544117 Simplifying x + 14.5 = 14.70544117 Reorder the terms: 14.5 + x = 14.70544117 Solving 14.5 + x = 14.70544117 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.5' to each side of the equation. 14.5 + -14.5 + x = 14.70544117 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + x = 14.70544117 + -14.5 x = 14.70544117 + -14.5 Combine like terms: 14.70544117 + -14.5 = 0.20544117 x = 0.20544117 Simplifying x = 0.20544117

Subproblem 2

x + 14.5 = -14.70544117 Simplifying x + 14.5 = -14.70544117 Reorder the terms: 14.5 + x = -14.70544117 Solving 14.5 + x = -14.70544117 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.5' to each side of the equation. 14.5 + -14.5 + x = -14.70544117 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + x = -14.70544117 + -14.5 x = -14.70544117 + -14.5 Combine like terms: -14.70544117 + -14.5 = -29.20544117 x = -29.20544117 Simplifying x = -29.20544117

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.20544117, -29.20544117}

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