5x^2+18x-180=0

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Solution for 5x^2+18x-180=0 equation:


Simplifying
5x2 + 18x + -180 = 0

Reorder the terms:
-180 + 18x + 5x2 = 0

Solving
-180 + 18x + 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'.
-36 + 3.6x + x2 = 0

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + 3.6x + 36 + x2 = 0 + 36

Reorder the terms:
-36 + 36 + 3.6x + x2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + 3.6x + x2 = 0 + 36
3.6x + x2 = 0 + 36

Combine like terms: 0 + 36 = 36
3.6x + x2 = 36

The x term is 3.6x.  Take half its coefficient (1.8).
Square it (3.24) and add it to both sides.

Add '3.24' to each side of the equation.
3.6x + 3.24 + x2 = 36 + 3.24

Reorder the terms:
3.24 + 3.6x + x2 = 36 + 3.24

Combine like terms: 36 + 3.24 = 39.24
3.24 + 3.6x + x2 = 39.24

Factor a perfect square on the left side:
(x + 1.8)(x + 1.8) = 39.24

Calculate the square root of the right side: 6.264183905

Break this problem into two subproblems by setting 
(x + 1.8) equal to 6.264183905 and -6.264183905.

Subproblem 1

x + 1.8 = 6.264183905 Simplifying x + 1.8 = 6.264183905 Reorder the terms: 1.8 + x = 6.264183905 Solving 1.8 + x = 6.264183905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + x = 6.264183905 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + x = 6.264183905 + -1.8 x = 6.264183905 + -1.8 Combine like terms: 6.264183905 + -1.8 = 4.464183905 x = 4.464183905 Simplifying x = 4.464183905

Subproblem 2

x + 1.8 = -6.264183905 Simplifying x + 1.8 = -6.264183905 Reorder the terms: 1.8 + x = -6.264183905 Solving 1.8 + x = -6.264183905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + x = -6.264183905 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + x = -6.264183905 + -1.8 x = -6.264183905 + -1.8 Combine like terms: -6.264183905 + -1.8 = -8.064183905 x = -8.064183905 Simplifying x = -8.064183905

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.464183905, -8.064183905}

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