-1.8x^2-9x+45=0

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Solution for -1.8x^2-9x+45=0 equation:


Simplifying
-1.8x2 + -9x + 45 = 0

Reorder the terms:
45 + -9x + -1.8x2 = 0

Solving
45 + -9x + -1.8x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1.8 the coefficient of the squared term: 

Divide each side by '-1.8'.
-25 + 5x + x2 = 0

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + 5x + 25 + x2 = 0 + 25

Reorder the terms:
-25 + 25 + 5x + x2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + 5x + x2 = 0 + 25
5x + x2 = 0 + 25

Combine like terms: 0 + 25 = 25
5x + x2 = 25

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 25 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 25 + 6.25

Combine like terms: 25 + 6.25 = 31.25
6.25 + 5x + x2 = 31.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 31.25

Calculate the square root of the right side: 5.590169944

Break this problem into two subproblems by setting 
(x + 2.5) equal to 5.590169944 and -5.590169944.

Subproblem 1

x + 2.5 = 5.590169944 Simplifying x + 2.5 = 5.590169944 Reorder the terms: 2.5 + x = 5.590169944 Solving 2.5 + x = 5.590169944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 5.590169944 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 5.590169944 + -2.5 x = 5.590169944 + -2.5 Combine like terms: 5.590169944 + -2.5 = 3.090169944 x = 3.090169944 Simplifying x = 3.090169944

Subproblem 2

x + 2.5 = -5.590169944 Simplifying x + 2.5 = -5.590169944 Reorder the terms: 2.5 + x = -5.590169944 Solving 2.5 + x = -5.590169944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -5.590169944 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -5.590169944 + -2.5 x = -5.590169944 + -2.5 Combine like terms: -5.590169944 + -2.5 = -8.090169944 x = -8.090169944 Simplifying x = -8.090169944

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.090169944, -8.090169944}

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