163.2+23.84x-16x^2=4

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Solution for 163.2+23.84x-16x^2=4 equation: 


Simplifying
163.2 + 23.84x + -16x2 = 4

Solving
163.2 + 23.84x + -16x2 = 4

Solving for variable 'x'.

Reorder the terms:
163.2 + -4 + 23.84x + -16x2 = 4 + -4

Combine like terms: 163.2 + -4 = 159.2
159.2 + 23.84x + -16x2 = 4 + -4

Combine like terms: 4 + -4 = 0
159.2 + 23.84x + -16x2 = 0

Begin completing the square.  Divide all terms by
-16 the coefficient of the squared term: 

Divide each side by '-16'.
-9.95 + -1.49x + x2 = 0

Move the constant term to the right:

Add '9.95' to each side of the equation.
-9.95 + -1.49x + 9.95 + x2 = 0 + 9.95

Reorder the terms:
-9.95 + 9.95 + -1.49x + x2 = 0 + 9.95

Combine like terms: -9.95 + 9.95 = 0.00
0.00 + -1.49x + x2 = 0 + 9.95
-1.49x + x2 = 0 + 9.95

Combine like terms: 0 + 9.95 = 9.95
-1.49x + x2 = 9.95

The x term is -1.49x.  Take half its coefficient (-0.745).
Square it (0.555025) and add it to both sides.

Add '0.555025' to each side of the equation.
-1.49x + 0.555025 + x2 = 9.95 + 0.555025

Reorder the terms:
0.555025 + -1.49x + x2 = 9.95 + 0.555025

Combine like terms: 9.95 + 0.555025 = 10.505025
0.555025 + -1.49x + x2 = 10.505025

Factor a perfect square on the left side:
(x + -0.745)(x + -0.745) = 10.505025

Calculate the square root of the right side: 3.241145631

Break this problem into two subproblems by setting 
(x + -0.745) equal to 3.241145631 and -3.241145631.


Subproblem 1
x + -0.745 = 3.241145631

Simplifying
x + -0.745 = 3.241145631

Reorder the terms:
-0.745 + x = 3.241145631

Solving
-0.745 + x = 3.241145631

Solving for variable 'x'.

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

Add '0.745' to each side of the equation.
-0.745 + 0.745 + x = 3.241145631 + 0.745

Combine like terms: -0.745 + 0.745 = 0.000
0.000 + x = 3.241145631 + 0.745
x = 3.241145631 + 0.745

Combine like terms: 3.241145631 + 0.745 = 3.986145631
x = 3.986145631

Simplifying
x = 3.986145631


Subproblem 2
x + -0.745 = -3.241145631

Simplifying
x + -0.745 = -3.241145631

Reorder the terms:
-0.745 + x = -3.241145631

Solving
-0.745 + x = -3.241145631

Solving for variable 'x'.

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

Add '0.745' to each side of the equation.
-0.745 + 0.745 + x = -3.241145631 + 0.745

Combine like terms: -0.745 + 0.745 = 0.000
0.000 + x = -3.241145631 + 0.745
x = -3.241145631 + 0.745

Combine like terms: -3.241145631 + 0.745 = -2.496145631
x = -2.496145631

Simplifying
x = -2.496145631


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.986145631, -2.496145631}

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