-16X^2+148X+7.8=0

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Solution for -16X^2+148X+7.8=0 equation: 


Simplifying
-16X2 + 148X + 7.8 = 0

Reorder the terms:
7.8 + 148X + -16X2 = 0

Solving
7.8 + 148X + -16X2 = 0

Solving for variable 'X'.

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

Divide each side by '-16'.
-0.4875 + -9.25X + X2 = 0

Move the constant term to the right:

Add '0.4875' to each side of the equation.
-0.4875 + -9.25X + 0.4875 + X2 = 0 + 0.4875

Reorder the terms:
-0.4875 + 0.4875 + -9.25X + X2 = 0 + 0.4875

Combine like terms: -0.4875 + 0.4875 = 0.0000
0.0000 + -9.25X + X2 = 0 + 0.4875
-9.25X + X2 = 0 + 0.4875

Combine like terms: 0 + 0.4875 = 0.4875
-9.25X + X2 = 0.4875

The X term is -9.25X.  Take half its coefficient (-4.625).
Square it (21.390625) and add it to both sides.

Add '21.390625' to each side of the equation.
-9.25X + 21.390625 + X2 = 0.4875 + 21.390625

Reorder the terms:
21.390625 + -9.25X + X2 = 0.4875 + 21.390625

Combine like terms: 0.4875 + 21.390625 = 21.878125
21.390625 + -9.25X + X2 = 21.878125

Factor a perfect square on the left side:
(X + -4.625)(X + -4.625) = 21.878125

Calculate the square root of the right side: 4.677405798

Break this problem into two subproblems by setting 
(X + -4.625) equal to 4.677405798 and -4.677405798.


Subproblem 1
X + -4.625 = 4.677405798

Simplifying
X + -4.625 = 4.677405798

Reorder the terms:
-4.625 + X = 4.677405798

Solving
-4.625 + X = 4.677405798

Solving for variable 'X'.

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

Add '4.625' to each side of the equation.
-4.625 + 4.625 + X = 4.677405798 + 4.625

Combine like terms: -4.625 + 4.625 = 0.000
0.000 + X = 4.677405798 + 4.625
X = 4.677405798 + 4.625

Combine like terms: 4.677405798 + 4.625 = 9.302405798
X = 9.302405798

Simplifying
X = 9.302405798


Subproblem 2
X + -4.625 = -4.677405798

Simplifying
X + -4.625 = -4.677405798

Reorder the terms:
-4.625 + X = -4.677405798

Solving
-4.625 + X = -4.677405798

Solving for variable 'X'.

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

Add '4.625' to each side of the equation.
-4.625 + 4.625 + X = -4.677405798 + 4.625

Combine like terms: -4.625 + 4.625 = 0.000
0.000 + X = -4.677405798 + 4.625
X = -4.677405798 + 4.625

Combine like terms: -4.677405798 + 4.625 = -0.052405798
X = -0.052405798

Simplifying
X = -0.052405798


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {9.302405798, -0.052405798}

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