40x^2-28x-7=0

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Solution for 40x^2-28x-7=0 equation: 


Simplifying
40x2 + -28x + -7 = 0

Reorder the terms:
-7 + -28x + 40x2 = 0

Solving
-7 + -28x + 40x2 = 0

Solving for variable 'x'.

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

Divide each side by '40'.
-0.175 + -0.7x + x2 = 0

Move the constant term to the right:

Add '0.175' to each side of the equation.
-0.175 + -0.7x + 0.175 + x2 = 0 + 0.175

Reorder the terms:
-0.175 + 0.175 + -0.7x + x2 = 0 + 0.175

Combine like terms: -0.175 + 0.175 = 0.000
0.000 + -0.7x + x2 = 0 + 0.175
-0.7x + x2 = 0 + 0.175

Combine like terms: 0 + 0.175 = 0.175
-0.7x + x2 = 0.175

The x term is -0.7x.  Take half its coefficient (-0.35).
Square it (0.1225) and add it to both sides.

Add '0.1225' to each side of the equation.
-0.7x + 0.1225 + x2 = 0.175 + 0.1225

Reorder the terms:
0.1225 + -0.7x + x2 = 0.175 + 0.1225

Combine like terms: 0.175 + 0.1225 = 0.2975
0.1225 + -0.7x + x2 = 0.2975

Factor a perfect square on the left side:
(x + -0.35)(x + -0.35) = 0.2975

Calculate the square root of the right side: 0.545435606

Break this problem into two subproblems by setting 
(x + -0.35) equal to 0.545435606 and -0.545435606.


Subproblem 1
x + -0.35 = 0.545435606

Simplifying
x + -0.35 = 0.545435606

Reorder the terms:
-0.35 + x = 0.545435606

Solving
-0.35 + x = 0.545435606

Solving for variable 'x'.

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

Add '0.35' to each side of the equation.
-0.35 + 0.35 + x = 0.545435606 + 0.35

Combine like terms: -0.35 + 0.35 = 0.00
0.00 + x = 0.545435606 + 0.35
x = 0.545435606 + 0.35

Combine like terms: 0.545435606 + 0.35 = 0.895435606
x = 0.895435606

Simplifying
x = 0.895435606


Subproblem 2
x + -0.35 = -0.545435606

Simplifying
x + -0.35 = -0.545435606

Reorder the terms:
-0.35 + x = -0.545435606

Solving
-0.35 + x = -0.545435606

Solving for variable 'x'.

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

Add '0.35' to each side of the equation.
-0.35 + 0.35 + x = -0.545435606 + 0.35

Combine like terms: -0.35 + 0.35 = 0.00
0.00 + x = -0.545435606 + 0.35
x = -0.545435606 + 0.35

Combine like terms: -0.545435606 + 0.35 = -0.195435606
x = -0.195435606

Simplifying
x = -0.195435606


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.895435606, -0.195435606}

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