x^2+13x-54=0

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Solution for x^2+13x-54=0 equation:


Simplifying
x2 + 13x + -54 = 0

Reorder the terms:
-54 + 13x + x2 = 0

Solving
-54 + 13x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '54' to each side of the equation.
-54 + 13x + 54 + x2 = 0 + 54

Reorder the terms:
-54 + 54 + 13x + x2 = 0 + 54

Combine like terms: -54 + 54 = 0
0 + 13x + x2 = 0 + 54
13x + x2 = 0 + 54

Combine like terms: 0 + 54 = 54
13x + x2 = 54

The x term is 13x.  Take half its coefficient (6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
13x + 42.25 + x2 = 54 + 42.25

Reorder the terms:
42.25 + 13x + x2 = 54 + 42.25

Combine like terms: 54 + 42.25 = 96.25
42.25 + 13x + x2 = 96.25

Factor a perfect square on the left side:
(x + 6.5)(x + 6.5) = 96.25

Calculate the square root of the right side: 9.810708435

Break this problem into two subproblems by setting 
(x + 6.5) equal to 9.810708435 and -9.810708435.

Subproblem 1

x + 6.5 = 9.810708435 Simplifying x + 6.5 = 9.810708435 Reorder the terms: 6.5 + x = 9.810708435 Solving 6.5 + x = 9.810708435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = 9.810708435 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 9.810708435 + -6.5 x = 9.810708435 + -6.5 Combine like terms: 9.810708435 + -6.5 = 3.310708435 x = 3.310708435 Simplifying x = 3.310708435

Subproblem 2

x + 6.5 = -9.810708435 Simplifying x + 6.5 = -9.810708435 Reorder the terms: 6.5 + x = -9.810708435 Solving 6.5 + x = -9.810708435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = -9.810708435 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -9.810708435 + -6.5 x = -9.810708435 + -6.5 Combine like terms: -9.810708435 + -6.5 = -16.310708435 x = -16.310708435 Simplifying x = -16.310708435

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.310708435, -16.310708435}

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