-4x^2+5x+8=0

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Solution for -4x^2+5x+8=0 equation: 


Simplifying
-4x2 + 5x + 8 = 0

Reorder the terms:
8 + 5x + -4x2 = 0

Solving
8 + 5x + -4x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-2 + -1.25x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -1.25x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + -1.25x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1.25x + x2 = 0 + 2
-1.25x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
-1.25x + x2 = 2

The x term is -1.25x.  Take half its coefficient (-0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
-1.25x + 0.390625 + x2 = 2 + 0.390625

Reorder the terms:
0.390625 + -1.25x + x2 = 2 + 0.390625

Combine like terms: 2 + 0.390625 = 2.390625
0.390625 + -1.25x + x2 = 2.390625

Factor a perfect square on the left side:
(x + -0.625)(x + -0.625) = 2.390625

Calculate the square root of the right side: 1.54616461

Break this problem into two subproblems by setting 
(x + -0.625) equal to 1.54616461 and -1.54616461.


Subproblem 1
x + -0.625 = 1.54616461

Simplifying
x + -0.625 = 1.54616461

Reorder the terms:
-0.625 + x = 1.54616461

Solving
-0.625 + x = 1.54616461

Solving for variable 'x'.

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

Add '0.625' to each side of the equation.
-0.625 + 0.625 + x = 1.54616461 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + x = 1.54616461 + 0.625
x = 1.54616461 + 0.625

Combine like terms: 1.54616461 + 0.625 = 2.17116461
x = 2.17116461

Simplifying
x = 2.17116461


Subproblem 2
x + -0.625 = -1.54616461

Simplifying
x + -0.625 = -1.54616461

Reorder the terms:
-0.625 + x = -1.54616461

Solving
-0.625 + x = -1.54616461

Solving for variable 'x'.

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

Add '0.625' to each side of the equation.
-0.625 + 0.625 + x = -1.54616461 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + x = -1.54616461 + 0.625
x = -1.54616461 + 0.625

Combine like terms: -1.54616461 + 0.625 = -0.92116461
x = -0.92116461

Simplifying
x = -0.92116461


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.17116461, -0.92116461}

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