2x(x+9)=15

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Solution for 2x(x+9)=15 equation:


Simplifying
2x(x + 9) = 15

Reorder the terms:
2x(9 + x) = 15
(9 * 2x + x * 2x) = 15
(18x + 2x2) = 15

Solving
18x + 2x2 = 15

Solving for variable 'x'.

Reorder the terms:
-15 + 18x + 2x2 = 15 + -15

Combine like terms: 15 + -15 = 0
-15 + 18x + 2x2 = 0

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

Divide each side by '2'.
-7.5 + 9x + x2 = 0

Move the constant term to the right:

Add '7.5' to each side of the equation.
-7.5 + 9x + 7.5 + x2 = 0 + 7.5

Reorder the terms:
-7.5 + 7.5 + 9x + x2 = 0 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + 9x + x2 = 0 + 7.5
9x + x2 = 0 + 7.5

Combine like terms: 0 + 7.5 = 7.5
9x + x2 = 7.5

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = 7.5 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 7.5 + 20.25

Combine like terms: 7.5 + 20.25 = 27.75
20.25 + 9x + x2 = 27.75

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 27.75

Calculate the square root of the right side: 5.267826876

Break this problem into two subproblems by setting 
(x + 4.5) equal to 5.267826876 and -5.267826876.

Subproblem 1

x + 4.5 = 5.267826876 Simplifying x + 4.5 = 5.267826876 Reorder the terms: 4.5 + x = 5.267826876 Solving 4.5 + x = 5.267826876 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 5.267826876 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 5.267826876 + -4.5 x = 5.267826876 + -4.5 Combine like terms: 5.267826876 + -4.5 = 0.767826876 x = 0.767826876 Simplifying x = 0.767826876

Subproblem 2

x + 4.5 = -5.267826876 Simplifying x + 4.5 = -5.267826876 Reorder the terms: 4.5 + x = -5.267826876 Solving 4.5 + x = -5.267826876 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -5.267826876 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -5.267826876 + -4.5 x = -5.267826876 + -4.5 Combine like terms: -5.267826876 + -4.5 = -9.767826876 x = -9.767826876 Simplifying x = -9.767826876

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.767826876, -9.767826876}

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