(2e+0.6)(2e+0.25)=3.02

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Solution for (2e+0.6)(2e+0.25)=3.02 equation:


Simplifying
(2e + 0.6)(2e + 0.25) = 3.02

Reorder the terms:
(0.6 + 2e)(2e + 0.25) = 3.02

Reorder the terms:
(0.6 + 2e)(0.25 + 2e) = 3.02

Multiply (0.6 + 2e) * (0.25 + 2e)
(0.6(0.25 + 2e) + 2e * (0.25 + 2e)) = 3.02
((0.25 * 0.6 + 2e * 0.6) + 2e * (0.25 + 2e)) = 3.02
((0.15 + 1.2e) + 2e * (0.25 + 2e)) = 3.02
(0.15 + 1.2e + (0.25 * 2e + 2e * 2e)) = 3.02
(0.15 + 1.2e + (0.5e + 4e2)) = 3.02

Combine like terms: 1.2e + 0.5e = 1.7e
(0.15 + 1.7e + 4e2) = 3.02

Solving
0.15 + 1.7e + 4e2 = 3.02

Solving for variable 'e'.

Reorder the terms:
0.15 + -3.02 + 1.7e + 4e2 = 3.02 + -3.02

Combine like terms: 0.15 + -3.02 = -2.87
-2.87 + 1.7e + 4e2 = 3.02 + -3.02

Combine like terms: 3.02 + -3.02 = 0.00
-2.87 + 1.7e + 4e2 = 0.00

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

Divide each side by '4'.
-0.7175 + 0.425e + e2 = 0.00

Move the constant term to the right:

Add '0.7175' to each side of the equation.
-0.7175 + 0.425e + 0.7175 + e2 = 0.00 + 0.7175

Reorder the terms:
-0.7175 + 0.7175 + 0.425e + e2 = 0.00 + 0.7175

Combine like terms: -0.7175 + 0.7175 = 0.0000
0.0000 + 0.425e + e2 = 0.00 + 0.7175
0.425e + e2 = 0.00 + 0.7175

Combine like terms: 0.00 + 0.7175 = 0.7175
0.425e + e2 = 0.7175

The e term is 0.425e.  Take half its coefficient (0.2125).
Square it (0.04515625) and add it to both sides.

Add '0.04515625' to each side of the equation.
0.425e + 0.04515625 + e2 = 0.7175 + 0.04515625

Reorder the terms:
0.04515625 + 0.425e + e2 = 0.7175 + 0.04515625

Combine like terms: 0.7175 + 0.04515625 = 0.76265625
0.04515625 + 0.425e + e2 = 0.76265625

Factor a perfect square on the left side:
(e + 0.2125)(e + 0.2125) = 0.76265625

Calculate the square root of the right side: 0.873301924

Break this problem into two subproblems by setting 
(e + 0.2125) equal to 0.873301924 and -0.873301924.

Subproblem 1

e + 0.2125 = 0.873301924 Simplifying e + 0.2125 = 0.873301924 Reorder the terms: 0.2125 + e = 0.873301924 Solving 0.2125 + e = 0.873301924 Solving for variable 'e'. Move all terms containing e to the left, all other terms to the right. Add '-0.2125' to each side of the equation. 0.2125 + -0.2125 + e = 0.873301924 + -0.2125 Combine like terms: 0.2125 + -0.2125 = 0.0000 0.0000 + e = 0.873301924 + -0.2125 e = 0.873301924 + -0.2125 Combine like terms: 0.873301924 + -0.2125 = 0.660801924 e = 0.660801924 Simplifying e = 0.660801924

Subproblem 2

e + 0.2125 = -0.873301924 Simplifying e + 0.2125 = -0.873301924 Reorder the terms: 0.2125 + e = -0.873301924 Solving 0.2125 + e = -0.873301924 Solving for variable 'e'. Move all terms containing e to the left, all other terms to the right. Add '-0.2125' to each side of the equation. 0.2125 + -0.2125 + e = -0.873301924 + -0.2125 Combine like terms: 0.2125 + -0.2125 = 0.0000 0.0000 + e = -0.873301924 + -0.2125 e = -0.873301924 + -0.2125 Combine like terms: -0.873301924 + -0.2125 = -1.085801924 e = -1.085801924 Simplifying e = -1.085801924

Solution

The solution to the problem is based on the solutions from the subproblems. e = {0.660801924, -1.085801924}

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