-28=7x-1.5x^2

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Solution for -28=7x-1.5x^2 equation: 


Simplifying
-28 = 7x + -1.5x2

Solving
-28 = 7x + -1.5x2

Solving for variable 'x'.

Reorder the terms:
-28 + -7x + 1.5x2 = 7x + -7x + -1.5x2 + 1.5x2

Combine like terms: 7x + -7x = 0
-28 + -7x + 1.5x2 = 0 + -1.5x2 + 1.5x2
-28 + -7x + 1.5x2 = -1.5x2 + 1.5x2

Combine like terms: -1.5x2 + 1.5x2 = 0.0
-28 + -7x + 1.5x2 = 0.0

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

Divide each side by '1.5'.
-18.66666667 + -4.666666667x + x2 = 0

Move the constant term to the right:

Add '18.66666667' to each side of the equation.
-18.66666667 + -4.666666667x + 18.66666667 + x2 = 0 + 18.66666667

Reorder the terms:
-18.66666667 + 18.66666667 + -4.666666667x + x2 = 0 + 18.66666667

Combine like terms: -18.66666667 + 18.66666667 = 0.00000000
0.00000000 + -4.666666667x + x2 = 0 + 18.66666667
-4.666666667x + x2 = 0 + 18.66666667

Combine like terms: 0 + 18.66666667 = 18.66666667
-4.666666667x + x2 = 18.66666667

The x term is -4.666666667x.  Take half its coefficient (-2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
-4.666666667x + 5.444444448 + x2 = 18.66666667 + 5.444444448

Reorder the terms:
5.444444448 + -4.666666667x + x2 = 18.66666667 + 5.444444448

Combine like terms: 18.66666667 + 5.444444448 = 24.111111118
5.444444448 + -4.666666667x + x2 = 24.111111118

Factor a perfect square on the left side:
(x + -2.333333334)(x + -2.333333334) = 24.111111118

Calculate the square root of the right side: 4.910306622

Break this problem into two subproblems by setting 
(x + -2.333333334) equal to 4.910306622 and -4.910306622.


Subproblem 1
x + -2.333333334 = 4.910306622

Simplifying
x + -2.333333334 = 4.910306622

Reorder the terms:
-2.333333334 + x = 4.910306622

Solving
-2.333333334 + x = 4.910306622

Solving for variable 'x'.

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

Add '2.333333334' to each side of the equation.
-2.333333334 + 2.333333334 + x = 4.910306622 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + x = 4.910306622 + 2.333333334
x = 4.910306622 + 2.333333334

Combine like terms: 4.910306622 + 2.333333334 = 7.243639956
x = 7.243639956

Simplifying
x = 7.243639956


Subproblem 2
x + -2.333333334 = -4.910306622

Simplifying
x + -2.333333334 = -4.910306622

Reorder the terms:
-2.333333334 + x = -4.910306622

Solving
-2.333333334 + x = -4.910306622

Solving for variable 'x'.

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

Add '2.333333334' to each side of the equation.
-2.333333334 + 2.333333334 + x = -4.910306622 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + x = -4.910306622 + 2.333333334
x = -4.910306622 + 2.333333334

Combine like terms: -4.910306622 + 2.333333334 = -2.576973288
x = -2.576973288

Simplifying
x = -2.576973288


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.243639956, -2.576973288}

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