5x^2+6x+6=20

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Solution for 5x^2+6x+6=20 equation:


Simplifying
5x2 + 6x + 6 = 20

Reorder the terms:
6 + 6x + 5x2 = 20

Solving
6 + 6x + 5x2 = 20

Solving for variable 'x'.

Reorder the terms:
6 + -20 + 6x + 5x2 = 20 + -20

Combine like terms: 6 + -20 = -14
-14 + 6x + 5x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-14 + 6x + 5x2 = 0

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

Divide each side by '5'.
-2.8 + 1.2x + x2 = 0

Move the constant term to the right:

Add '2.8' to each side of the equation.
-2.8 + 1.2x + 2.8 + x2 = 0 + 2.8

Reorder the terms:
-2.8 + 2.8 + 1.2x + x2 = 0 + 2.8

Combine like terms: -2.8 + 2.8 = 0.0
0.0 + 1.2x + x2 = 0 + 2.8
1.2x + x2 = 0 + 2.8

Combine like terms: 0 + 2.8 = 2.8
1.2x + x2 = 2.8

The x term is 1.2x.  Take half its coefficient (0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
1.2x + 0.36 + x2 = 2.8 + 0.36

Reorder the terms:
0.36 + 1.2x + x2 = 2.8 + 0.36

Combine like terms: 2.8 + 0.36 = 3.16
0.36 + 1.2x + x2 = 3.16

Factor a perfect square on the left side:
(x + 0.6)(x + 0.6) = 3.16

Calculate the square root of the right side: 1.777638883

Break this problem into two subproblems by setting 
(x + 0.6) equal to 1.777638883 and -1.777638883.

Subproblem 1

x + 0.6 = 1.777638883 Simplifying x + 0.6 = 1.777638883 Reorder the terms: 0.6 + x = 1.777638883 Solving 0.6 + x = 1.777638883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = 1.777638883 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = 1.777638883 + -0.6 x = 1.777638883 + -0.6 Combine like terms: 1.777638883 + -0.6 = 1.177638883 x = 1.177638883 Simplifying x = 1.177638883

Subproblem 2

x + 0.6 = -1.777638883 Simplifying x + 0.6 = -1.777638883 Reorder the terms: 0.6 + x = -1.777638883 Solving 0.6 + x = -1.777638883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = -1.777638883 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = -1.777638883 + -0.6 x = -1.777638883 + -0.6 Combine like terms: -1.777638883 + -0.6 = -2.377638883 x = -2.377638883 Simplifying x = -2.377638883

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.177638883, -2.377638883}

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