9.04=(0.55+2x)(0.3+2x)

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Solution for 9.04=(0.55+2x)(0.3+2x) equation:


Simplifying
9.04 = (0.55 + 2x)(0.3 + 2x)

Multiply (0.55 + 2x) * (0.3 + 2x)
9.04 = (0.55(0.3 + 2x) + 2x * (0.3 + 2x))
9.04 = ((0.3 * 0.55 + 2x * 0.55) + 2x * (0.3 + 2x))
9.04 = ((0.165 + 1.1x) + 2x * (0.3 + 2x))
9.04 = (0.165 + 1.1x + (0.3 * 2x + 2x * 2x))
9.04 = (0.165 + 1.1x + (0.6x + 4x2))

Combine like terms: 1.1x + 0.6x = 1.7x
9.04 = (0.165 + 1.7x + 4x2)

Solving
9.04 = 0.165 + 1.7x + 4x2

Solving for variable 'x'.

Combine like terms: 9.04 + -0.165 = 8.875
8.875 + -1.7x + -4x2 = 0.165 + 1.7x + 4x2 + -0.165 + -1.7x + -4x2

Reorder the terms:
8.875 + -1.7x + -4x2 = 0.165 + -0.165 + 1.7x + -1.7x + 4x2 + -4x2

Combine like terms: 0.165 + -0.165 = 0.000
8.875 + -1.7x + -4x2 = 0.000 + 1.7x + -1.7x + 4x2 + -4x2
8.875 + -1.7x + -4x2 = 1.7x + -1.7x + 4x2 + -4x2

Combine like terms: 1.7x + -1.7x = 0.0
8.875 + -1.7x + -4x2 = 0.0 + 4x2 + -4x2
8.875 + -1.7x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
8.875 + -1.7x + -4x2 = 0

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

Divide each side by '-4'.
-2.21875 + 0.425x + x2 = 0

Move the constant term to the right:

Add '2.21875' to each side of the equation.
-2.21875 + 0.425x + 2.21875 + x2 = 0 + 2.21875

Reorder the terms:
-2.21875 + 2.21875 + 0.425x + x2 = 0 + 2.21875

Combine like terms: -2.21875 + 2.21875 = 0.00000
0.00000 + 0.425x + x2 = 0 + 2.21875
0.425x + x2 = 0 + 2.21875

Combine like terms: 0 + 2.21875 = 2.21875
0.425x + x2 = 2.21875

The x term is 0.425x.  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.
0.425x + 0.04515625 + x2 = 2.21875 + 0.04515625

Reorder the terms:
0.04515625 + 0.425x + x2 = 2.21875 + 0.04515625

Combine like terms: 2.21875 + 0.04515625 = 2.26390625
0.04515625 + 0.425x + x2 = 2.26390625

Factor a perfect square on the left side:
(x + 0.2125)(x + 0.2125) = 2.26390625

Calculate the square root of the right side: 1.504628276

Break this problem into two subproblems by setting 
(x + 0.2125) equal to 1.504628276 and -1.504628276.

Subproblem 1

x + 0.2125 = 1.504628276 Simplifying x + 0.2125 = 1.504628276 Reorder the terms: 0.2125 + x = 1.504628276 Solving 0.2125 + x = 1.504628276 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2125' to each side of the equation. 0.2125 + -0.2125 + x = 1.504628276 + -0.2125 Combine like terms: 0.2125 + -0.2125 = 0.0000 0.0000 + x = 1.504628276 + -0.2125 x = 1.504628276 + -0.2125 Combine like terms: 1.504628276 + -0.2125 = 1.292128276 x = 1.292128276 Simplifying x = 1.292128276

Subproblem 2

x + 0.2125 = -1.504628276 Simplifying x + 0.2125 = -1.504628276 Reorder the terms: 0.2125 + x = -1.504628276 Solving 0.2125 + x = -1.504628276 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2125' to each side of the equation. 0.2125 + -0.2125 + x = -1.504628276 + -0.2125 Combine like terms: 0.2125 + -0.2125 = 0.0000 0.0000 + x = -1.504628276 + -0.2125 x = -1.504628276 + -0.2125 Combine like terms: -1.504628276 + -0.2125 = -1.717128276 x = -1.717128276 Simplifying x = -1.717128276

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.292128276, -1.717128276}

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