7.5x^2-6x=9.8

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Solution for 7.5x^2-6x=9.8 equation:


Simplifying
7.5x2 + -6x = 9.8

Reorder the terms:
-6x + 7.5x2 = 9.8

Solving
-6x + 7.5x2 = 9.8

Solving for variable 'x'.

Reorder the terms:
-9.8 + -6x + 7.5x2 = 9.8 + -9.8

Combine like terms: 9.8 + -9.8 = 0.0
-9.8 + -6x + 7.5x2 = 0.0

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

Divide each side by '7.5'.
-1.306666667 + -0.8x + x2 = 0

Move the constant term to the right:

Add '1.306666667' to each side of the equation.
-1.306666667 + -0.8x + 1.306666667 + x2 = 0 + 1.306666667

Reorder the terms:
-1.306666667 + 1.306666667 + -0.8x + x2 = 0 + 1.306666667

Combine like terms: -1.306666667 + 1.306666667 = 0.000000000
0.000000000 + -0.8x + x2 = 0 + 1.306666667
-0.8x + x2 = 0 + 1.306666667

Combine like terms: 0 + 1.306666667 = 1.306666667
-0.8x + x2 = 1.306666667

The x term is -0.8x.  Take half its coefficient (-0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
-0.8x + 0.16 + x2 = 1.306666667 + 0.16

Reorder the terms:
0.16 + -0.8x + x2 = 1.306666667 + 0.16

Combine like terms: 1.306666667 + 0.16 = 1.466666667
0.16 + -0.8x + x2 = 1.466666667

Factor a perfect square on the left side:
(x + -0.4)(x + -0.4) = 1.466666667

Calculate the square root of the right side: 1.211060142

Break this problem into two subproblems by setting 
(x + -0.4) equal to 1.211060142 and -1.211060142.


Subproblem 1
x + -0.4 = 1.211060142

Simplifying
x + -0.4 = 1.211060142

Reorder the terms:
-0.4 + x = 1.211060142

Solving
-0.4 + x = 1.211060142

Solving for variable 'x'.

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

Add '0.4' to each side of the equation.
-0.4 + 0.4 + x = 1.211060142 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + x = 1.211060142 + 0.4
x = 1.211060142 + 0.4

Combine like terms: 1.211060142 + 0.4 = 1.611060142
x = 1.611060142

Simplifying
x = 1.611060142


Subproblem 2
x + -0.4 = -1.211060142

Simplifying
x + -0.4 = -1.211060142

Reorder the terms:
-0.4 + x = -1.211060142

Solving
-0.4 + x = -1.211060142

Solving for variable 'x'.

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

Add '0.4' to each side of the equation.
-0.4 + 0.4 + x = -1.211060142 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + x = -1.211060142 + 0.4
x = -1.211060142 + 0.4

Combine like terms: -1.211060142 + 0.4 = -0.811060142
x = -0.811060142

Simplifying
x = -0.811060142


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.611060142, -0.811060142}

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