-4x^2-3x+5=0

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Solution for -4x^2-3x+5=0 equation: 


Simplifying
-4x2 + -3x + 5 = 0

Reorder the terms:
5 + -3x + -4x2 = 0

Solving
5 + -3x + -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'.
-1.25 + 0.75x + x2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + 0.75x + 1.25 + x2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + 0.75x + x2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + 0.75x + x2 = 0 + 1.25
0.75x + x2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
0.75x + x2 = 1.25

The x term is 0.75x.  Take half its coefficient (0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
0.75x + 0.140625 + x2 = 1.25 + 0.140625

Reorder the terms:
0.140625 + 0.75x + x2 = 1.25 + 0.140625

Combine like terms: 1.25 + 0.140625 = 1.390625
0.140625 + 0.75x + x2 = 1.390625

Factor a perfect square on the left side:
(x + 0.375)(x + 0.375) = 1.390625

Calculate the square root of the right side: 1.179247642

Break this problem into two subproblems by setting 
(x + 0.375) equal to 1.179247642 and -1.179247642.


Subproblem 1
x + 0.375 = 1.179247642

Simplifying
x + 0.375 = 1.179247642

Reorder the terms:
0.375 + x = 1.179247642

Solving
0.375 + x = 1.179247642

Solving for variable 'x'.

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

Add '-0.375' to each side of the equation.
0.375 + -0.375 + x = 1.179247642 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + x = 1.179247642 + -0.375
x = 1.179247642 + -0.375

Combine like terms: 1.179247642 + -0.375 = 0.804247642
x = 0.804247642

Simplifying
x = 0.804247642


Subproblem 2
x + 0.375 = -1.179247642

Simplifying
x + 0.375 = -1.179247642

Reorder the terms:
0.375 + x = -1.179247642

Solving
0.375 + x = -1.179247642

Solving for variable 'x'.

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

Add '-0.375' to each side of the equation.
0.375 + -0.375 + x = -1.179247642 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + x = -1.179247642 + -0.375
x = -1.179247642 + -0.375

Combine like terms: -1.179247642 + -0.375 = -1.554247642
x = -1.554247642

Simplifying
x = -1.554247642


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.804247642, -1.554247642}

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