0.6(x+5)=x^2+3.09

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Solution for 0.6(x+5)=x^2+3.09 equation:


Simplifying
0.6(x + 5) = x2 + 3.09

Reorder the terms:
0.6(5 + x) = x2 + 3.09
(5 * 0.6 + x * 0.6) = x2 + 3.09
(3 + 0.6x) = x2 + 3.09

Reorder the terms:
3 + 0.6x = 3.09 + x2

Solving
3 + 0.6x = 3.09 + x2

Solving for variable 'x'.

Reorder the terms:
3 + -3.09 + 0.6x + -1x2 = 3.09 + x2 + -3.09 + -1x2

Combine like terms: 3 + -3.09 = -0.09
-0.09 + 0.6x + -1x2 = 3.09 + x2 + -3.09 + -1x2

Reorder the terms:
-0.09 + 0.6x + -1x2 = 3.09 + -3.09 + x2 + -1x2

Combine like terms: 3.09 + -3.09 = 0.00
-0.09 + 0.6x + -1x2 = 0.00 + x2 + -1x2
-0.09 + 0.6x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-0.09 + 0.6x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
0.09 + -0.6x + x2 = 0

Move the constant term to the right:

Add '-0.09' to each side of the equation.
0.09 + -0.6x + -0.09 + x2 = 0 + -0.09

Reorder the terms:
0.09 + -0.09 + -0.6x + x2 = 0 + -0.09

Combine like terms: 0.09 + -0.09 = 0.00
0.00 + -0.6x + x2 = 0 + -0.09
-0.6x + x2 = 0 + -0.09

Combine like terms: 0 + -0.09 = -0.09
-0.6x + x2 = -0.09

The x term is -0.6x.  Take half its coefficient (-0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
-0.6x + 0.09 + x2 = -0.09 + 0.09

Reorder the terms:
0.09 + -0.6x + x2 = -0.09 + 0.09

Combine like terms: -0.09 + 0.09 = 0.00
0.09 + -0.6x + x2 = 0.00

Factor a perfect square on the left side:
(x + -0.3)(x + -0.3) = 0.00

Calculate the square root of the right side: 0.00

Break this problem into two subproblems by setting 
(x + -0.3) equal to 0.00 and 0.00.

Subproblem 1

x + -0.3 = 0.00 Simplifying x + -0.3 = 0.00 Reorder the terms: -0.3 + x = 0.00 Solving -0.3 + x = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = 0.00 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 0.00 + 0.3 x = 0.00 + 0.3 Combine like terms: 0.00 + 0.3 = 0.3 x = 0.3 Simplifying x = 0.3

Subproblem 2

x + -0.3 = 0.00 Simplifying x + -0.3 = 0.00 Reorder the terms: -0.3 + x = 0.00 Solving -0.3 + x = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = 0.00 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 0.00 + 0.3 x = 0.00 + 0.3 Combine like terms: 0.00 + 0.3 = 0.3 x = 0.3 Simplifying x = 0.3

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.3, 0.3}

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