-8x^2+43x-30=0

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Solution for -8x^2+43x-30=0 equation: 


Simplifying
-8x2 + 43x + -30 = 0

Reorder the terms:
-30 + 43x + -8x2 = 0

Solving
-30 + 43x + -8x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
3.75 + -5.375x + x2 = 0

Move the constant term to the right:

Add '-3.75' to each side of the equation.
3.75 + -5.375x + -3.75 + x2 = 0 + -3.75

Reorder the terms:
3.75 + -3.75 + -5.375x + x2 = 0 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + -5.375x + x2 = 0 + -3.75
-5.375x + x2 = 0 + -3.75

Combine like terms: 0 + -3.75 = -3.75
-5.375x + x2 = -3.75

The x term is -5.375x.  Take half its coefficient (-2.6875).
Square it (7.22265625) and add it to both sides.

Add '7.22265625' to each side of the equation.
-5.375x + 7.22265625 + x2 = -3.75 + 7.22265625

Reorder the terms:
7.22265625 + -5.375x + x2 = -3.75 + 7.22265625

Combine like terms: -3.75 + 7.22265625 = 3.47265625
7.22265625 + -5.375x + x2 = 3.47265625

Factor a perfect square on the left side:
(x + -2.6875)(x + -2.6875) = 3.47265625

Calculate the square root of the right side: 1.863506439

Break this problem into two subproblems by setting 
(x + -2.6875) equal to 1.863506439 and -1.863506439.


Subproblem 1
x + -2.6875 = 1.863506439

Simplifying
x + -2.6875 = 1.863506439

Reorder the terms:
-2.6875 + x = 1.863506439

Solving
-2.6875 + x = 1.863506439

Solving for variable 'x'.

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

Add '2.6875' to each side of the equation.
-2.6875 + 2.6875 + x = 1.863506439 + 2.6875

Combine like terms: -2.6875 + 2.6875 = 0.0000
0.0000 + x = 1.863506439 + 2.6875
x = 1.863506439 + 2.6875

Combine like terms: 1.863506439 + 2.6875 = 4.551006439
x = 4.551006439

Simplifying
x = 4.551006439


Subproblem 2
x + -2.6875 = -1.863506439

Simplifying
x + -2.6875 = -1.863506439

Reorder the terms:
-2.6875 + x = -1.863506439

Solving
-2.6875 + x = -1.863506439

Solving for variable 'x'.

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

Add '2.6875' to each side of the equation.
-2.6875 + 2.6875 + x = -1.863506439 + 2.6875

Combine like terms: -2.6875 + 2.6875 = 0.0000
0.0000 + x = -1.863506439 + 2.6875
x = -1.863506439 + 2.6875

Combine like terms: -1.863506439 + 2.6875 = 0.823993561
x = 0.823993561

Simplifying
x = 0.823993561


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.551006439, 0.823993561}

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