x^2+5.5x+7.5625=

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Solution for x^2+5.5x+7.5625= equation:


Simplifying
x2 + 5.5x + 7.5625 = 0

Reorder the terms:
7.5625 + 5.5x + x2 = 0

Solving
7.5625 + 5.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-7.5625' to each side of the equation.
7.5625 + 5.5x + -7.5625 + x2 = 0 + -7.5625

Reorder the terms:
7.5625 + -7.5625 + 5.5x + x2 = 0 + -7.5625

Combine like terms: 7.5625 + -7.5625 = 0.0000
0.0000 + 5.5x + x2 = 0 + -7.5625
5.5x + x2 = 0 + -7.5625

Combine like terms: 0 + -7.5625 = -7.5625
5.5x + x2 = -7.5625

The x term is 5.5x.  Take half its coefficient (2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
5.5x + 7.5625 + x2 = -7.5625 + 7.5625

Reorder the terms:
7.5625 + 5.5x + x2 = -7.5625 + 7.5625

Combine like terms: -7.5625 + 7.5625 = 0.0000
7.5625 + 5.5x + x2 = 0.0000

Factor a perfect square on the left side:
(x + 2.75)(x + 2.75) = 0.0000

Calculate the square root of the right side: 0.0000

Break this problem into two subproblems by setting 
(x + 2.75) equal to 0.0000 and 0.0000.

Subproblem 1

x + 2.75 = 0.0000 Simplifying x + 2.75 = 0.0000 Reorder the terms: 2.75 + x = 0.0000 Solving 2.75 + x = 0.0000 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = 0.0000 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = 0.0000 + -2.75 x = 0.0000 + -2.75 Combine like terms: 0.0000 + -2.75 = -2.75 x = -2.75 Simplifying x = -2.75

Subproblem 2

x + 2.75 = 0.0000 Simplifying x + 2.75 = 0.0000 Reorder the terms: 2.75 + x = 0.0000 Solving 2.75 + x = 0.0000 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = 0.0000 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = 0.0000 + -2.75 x = 0.0000 + -2.75 Combine like terms: 0.0000 + -2.75 = -2.75 x = -2.75 Simplifying x = -2.75

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-2.75, -2.75}

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