4x(2x+9)=-15

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Solution for 4x(2x+9)=-15 equation:


Simplifying
4x(2x + 9) = -15

Reorder the terms:
4x(9 + 2x) = -15
(9 * 4x + 2x * 4x) = -15
(36x + 8x2) = -15

Solving
36x + 8x2 = -15

Solving for variable 'x'.

Reorder the terms:
15 + 36x + 8x2 = -15 + 15

Combine like terms: -15 + 15 = 0
15 + 36x + 8x2 = 0

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

Divide each side by '8'.
1.875 + 4.5x + x2 = 0

Move the constant term to the right:

Add '-1.875' to each side of the equation.
1.875 + 4.5x + -1.875 + x2 = 0 + -1.875

Reorder the terms:
1.875 + -1.875 + 4.5x + x2 = 0 + -1.875

Combine like terms: 1.875 + -1.875 = 0.000
0.000 + 4.5x + x2 = 0 + -1.875
4.5x + x2 = 0 + -1.875

Combine like terms: 0 + -1.875 = -1.875
4.5x + x2 = -1.875

The x term is 4.5x.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5x + 5.0625 + x2 = -1.875 + 5.0625

Reorder the terms:
5.0625 + 4.5x + x2 = -1.875 + 5.0625

Combine like terms: -1.875 + 5.0625 = 3.1875
5.0625 + 4.5x + x2 = 3.1875

Factor a perfect square on the left side:
(x + 2.25)(x + 2.25) = 3.1875

Calculate the square root of the right side: 1.785357107

Break this problem into two subproblems by setting 
(x + 2.25) equal to 1.785357107 and -1.785357107.

Subproblem 1

x + 2.25 = 1.785357107 Simplifying x + 2.25 = 1.785357107 Reorder the terms: 2.25 + x = 1.785357107 Solving 2.25 + x = 1.785357107 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 1.785357107 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 1.785357107 + -2.25 x = 1.785357107 + -2.25 Combine like terms: 1.785357107 + -2.25 = -0.464642893 x = -0.464642893 Simplifying x = -0.464642893

Subproblem 2

x + 2.25 = -1.785357107 Simplifying x + 2.25 = -1.785357107 Reorder the terms: 2.25 + x = -1.785357107 Solving 2.25 + x = -1.785357107 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -1.785357107 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -1.785357107 + -2.25 x = -1.785357107 + -2.25 Combine like terms: -1.785357107 + -2.25 = -4.035357107 x = -4.035357107 Simplifying x = -4.035357107

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.464642893, -4.035357107}

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