5x^2-20x-45=0

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Solution for 5x^2-20x-45=0 equation: 


Simplifying
5x2 + -20x + -45 = 0

Reorder the terms:
-45 + -20x + 5x2 = 0

Solving
-45 + -20x + 5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-9 + -4x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-9 + -4x + x2)' equal to zero and attempt to solve:

Simplifying
-9 + -4x + x2 = 0

Solving
-9 + -4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -4x + 9 + x2 = 0 + 9

Reorder the terms:
-9 + 9 + -4x + x2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -4x + x2 = 0 + 9
-4x + x2 = 0 + 9

Combine like terms: 0 + 9 = 9
-4x + x2 = 9

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 9 + 4

Reorder the terms:
4 + -4x + x2 = 9 + 4

Combine like terms: 9 + 4 = 13
4 + -4x + x2 = 13

Factor a perfect square on the left side:
(x + -2)(x + -2) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(x + -2) equal to 3.605551275 and -3.605551275.


Subproblem 1
x + -2 = 3.605551275

Simplifying
x + -2 = 3.605551275

Reorder the terms:
-2 + x = 3.605551275

Solving
-2 + x = 3.605551275

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + x = 3.605551275 + 2

Combine like terms: -2 + 2 = 0
0 + x = 3.605551275 + 2
x = 3.605551275 + 2

Combine like terms: 3.605551275 + 2 = 5.605551275
x = 5.605551275

Simplifying
x = 5.605551275


Subproblem 2
x + -2 = -3.605551275

Simplifying
x + -2 = -3.605551275

Reorder the terms:
-2 + x = -3.605551275

Solving
-2 + x = -3.605551275

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + x = -3.605551275 + 2

Combine like terms: -2 + 2 = 0
0 + x = -3.605551275 + 2
x = -3.605551275 + 2

Combine like terms: -3.605551275 + 2 = -1.605551275
x = -1.605551275

Simplifying
x = -1.605551275


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.605551275, -1.605551275}
Solution
x = {5.605551275, -1.605551275}

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