2.4525x^2-17.9523x-3.3489=0

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Solution for 2.4525x^2-17.9523x-3.3489=0 equation:


Simplifying
2.4525x2 + -17.9523x + -3.3489 = 0

Reorder the terms:
-3.3489 + -17.9523x + 2.4525x2 = 0

Solving
-3.3489 + -17.9523x + 2.4525x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
2.4525 the coefficient of the squared term: 

Divide each side by '2.4525'.
-1.365504587 + -7.32x + x2 = 0

Move the constant term to the right:

Add '1.365504587' to each side of the equation.
-1.365504587 + -7.32x + 1.365504587 + x2 = 0 + 1.365504587

Reorder the terms:
-1.365504587 + 1.365504587 + -7.32x + x2 = 0 + 1.365504587

Combine like terms: -1.365504587 + 1.365504587 = 0.000000000
0.000000000 + -7.32x + x2 = 0 + 1.365504587
-7.32x + x2 = 0 + 1.365504587

Combine like terms: 0 + 1.365504587 = 1.365504587
-7.32x + x2 = 1.365504587

The x term is -7.32x.  Take half its coefficient (-3.66).
Square it (13.3956) and add it to both sides.

Add '13.3956' to each side of the equation.
-7.32x + 13.3956 + x2 = 1.365504587 + 13.3956

Reorder the terms:
13.3956 + -7.32x + x2 = 1.365504587 + 13.3956

Combine like terms: 1.365504587 + 13.3956 = 14.761104587
13.3956 + -7.32x + x2 = 14.761104587

Factor a perfect square on the left side:
(x + -3.66)(x + -3.66) = 14.761104587

Calculate the square root of the right side: 3.842018296

Break this problem into two subproblems by setting 
(x + -3.66) equal to 3.842018296 and -3.842018296.


Subproblem 1
x + -3.66 = 3.842018296

Simplifying
x + -3.66 = 3.842018296

Reorder the terms:
-3.66 + x = 3.842018296

Solving
-3.66 + x = 3.842018296

Solving for variable 'x'.

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

Add '3.66' to each side of the equation.
-3.66 + 3.66 + x = 3.842018296 + 3.66

Combine like terms: -3.66 + 3.66 = 0.00
0.00 + x = 3.842018296 + 3.66
x = 3.842018296 + 3.66

Combine like terms: 3.842018296 + 3.66 = 7.502018296
x = 7.502018296

Simplifying
x = 7.502018296


Subproblem 2
x + -3.66 = -3.842018296

Simplifying
x + -3.66 = -3.842018296

Reorder the terms:
-3.66 + x = -3.842018296

Solving
-3.66 + x = -3.842018296

Solving for variable 'x'.

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

Add '3.66' to each side of the equation.
-3.66 + 3.66 + x = -3.842018296 + 3.66

Combine like terms: -3.66 + 3.66 = 0.00
0.00 + x = -3.842018296 + 3.66
x = -3.842018296 + 3.66

Combine like terms: -3.842018296 + 3.66 = -0.182018296
x = -0.182018296

Simplifying
x = -0.182018296


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.502018296, -0.182018296}

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