5x^2+15x-54=0

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Solution for 5x^2+15x-54=0 equation:


Simplifying
5x2 + 15x + -54 = 0

Reorder the terms:
-54 + 15x + 5x2 = 0

Solving
-54 + 15x + 5x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
-10.8 + 3x + x2 = 0

Move the constant term to the right:

Add '10.8' to each side of the equation.
-10.8 + 3x + 10.8 + x2 = 0 + 10.8

Reorder the terms:
-10.8 + 10.8 + 3x + x2 = 0 + 10.8

Combine like terms: -10.8 + 10.8 = 0.0
0.0 + 3x + x2 = 0 + 10.8
3x + x2 = 0 + 10.8

Combine like terms: 0 + 10.8 = 10.8
3x + x2 = 10.8

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 = 10.8 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 10.8 + 2.25

Combine like terms: 10.8 + 2.25 = 13.05
2.25 + 3x + x2 = 13.05

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 13.05

Calculate the square root of the right side: 3.612478374

Break this problem into two subproblems by setting 
(x + 1.5) equal to 3.612478374 and -3.612478374.

Subproblem 1

x + 1.5 = 3.612478374 Simplifying x + 1.5 = 3.612478374 Reorder the terms: 1.5 + x = 3.612478374 Solving 1.5 + x = 3.612478374 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 = 3.612478374 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 3.612478374 + -1.5 x = 3.612478374 + -1.5 Combine like terms: 3.612478374 + -1.5 = 2.112478374 x = 2.112478374 Simplifying x = 2.112478374

Subproblem 2

x + 1.5 = -3.612478374 Simplifying x + 1.5 = -3.612478374 Reorder the terms: 1.5 + x = -3.612478374 Solving 1.5 + x = -3.612478374 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 = -3.612478374 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -3.612478374 + -1.5 x = -3.612478374 + -1.5 Combine like terms: -3.612478374 + -1.5 = -5.112478374 x = -5.112478374 Simplifying x = -5.112478374

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.112478374, -5.112478374}

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