2x^2+3x-94=0

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Solution for 2x^2+3x-94=0 equation: 


Simplifying
2x2 + 3x + -94 = 0

Reorder the terms:
-94 + 3x + 2x2 = 0

Solving
-94 + 3x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-47 + 1.5x + x2 = 0

Move the constant term to the right:

Add '47' to each side of the equation.
-47 + 1.5x + 47 + x2 = 0 + 47

Reorder the terms:
-47 + 47 + 1.5x + x2 = 0 + 47

Combine like terms: -47 + 47 = 0
0 + 1.5x + x2 = 0 + 47
1.5x + x2 = 0 + 47

Combine like terms: 0 + 47 = 47
1.5x + x2 = 47

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = 47 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 47 + 0.5625

Combine like terms: 47 + 0.5625 = 47.5625
0.5625 + 1.5x + x2 = 47.5625

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 47.5625

Calculate the square root of the right side: 6.896557112

Break this problem into two subproblems by setting 
(x + 0.75) equal to 6.896557112 and -6.896557112.


Subproblem 1
x + 0.75 = 6.896557112

Simplifying
x + 0.75 = 6.896557112

Reorder the terms:
0.75 + x = 6.896557112

Solving
0.75 + x = 6.896557112

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = 6.896557112 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = 6.896557112 + -0.75
x = 6.896557112 + -0.75

Combine like terms: 6.896557112 + -0.75 = 6.146557112
x = 6.146557112

Simplifying
x = 6.146557112


Subproblem 2
x + 0.75 = -6.896557112

Simplifying
x + 0.75 = -6.896557112

Reorder the terms:
0.75 + x = -6.896557112

Solving
0.75 + x = -6.896557112

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = -6.896557112 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = -6.896557112 + -0.75
x = -6.896557112 + -0.75

Combine like terms: -6.896557112 + -0.75 = -7.646557112
x = -7.646557112

Simplifying
x = -7.646557112


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.146557112, -7.646557112}

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