40x^2+2x-30=0

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Solution for 40x^2+2x-30=0 equation: 


Simplifying
40x2 + 2x + -30 = 0

Reorder the terms:
-30 + 2x + 40x2 = 0

Solving
-30 + 2x + 40x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + x + 20x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-15 + x + 20x2)' equal to zero and attempt to solve:

Simplifying
-15 + x + 20x2 = 0

Solving
-15 + x + 20x2 = 0

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

Divide each side by '20'.
-0.75 + 0.05x + x2 = 0.0

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + 0.05x + 0.75 + x2 = 0.0 + 0.75

Reorder the terms:
-0.75 + 0.75 + 0.05x + x2 = 0.0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + 0.05x + x2 = 0.0 + 0.75
0.05x + x2 = 0.0 + 0.75

Combine like terms: 0.0 + 0.75 = 0.75
0.05x + x2 = 0.75

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.05x + 0.25 + x2 = 0.75 + 0.25

Reorder the terms:
0.25 + 0.05x + x2 = 0.75 + 0.25

Combine like terms: 0.75 + 0.25 = 1
0.25 + 0.05x + x2 = 1

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 1

Calculate the square root of the right side: 1

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1 and -1.


Subproblem 1
x + 0.5 = 1

Simplifying
x + 0.5 = 1

Reorder the terms:
0.5 + x = 1

Solving
0.5 + x = 1

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 1 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 1 + -0.5
x = 1 + -0.5

Combine like terms: 1 + -0.5 = 0.5
x = 0.5

Simplifying
x = 0.5


Subproblem 2
x + 0.5 = -1

Simplifying
x + 0.5 = -1

Reorder the terms:
0.5 + x = -1

Solving
0.5 + x = -1

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -1 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -1 + -0.5
x = -1 + -0.5

Combine like terms: -1 + -0.5 = -1.5
x = -1.5

Simplifying
x = -1.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.5, -1.5}
Solution
x = {0.5, -1.5}

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