.4x(x-9)=.3(x+4)

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Solution for .4x(x-9)=.3(x+4) equation:


Simplifying
0.4x(x + -9) = 0.3(x + 4)

Reorder the terms:
0.4x(-9 + x) = 0.3(x + 4)
(-9 * 0.4x + x * 0.4x) = 0.3(x + 4)
(-3.6x + 0.4x2) = 0.3(x + 4)

Reorder the terms:
-3.6x + 0.4x2 = 0.3(4 + x)
-3.6x + 0.4x2 = (4 * 0.3 + x * 0.3)
-3.6x + 0.4x2 = (1.2 + 0.3x)

Solving
-3.6x + 0.4x2 = 1.2 + 0.3x

Solving for variable 'x'.

Reorder the terms:
-1.2 + -3.6x + -0.3x + 0.4x2 = 1.2 + 0.3x + -1.2 + -0.3x

Combine like terms: -3.6x + -0.3x = -3.9x
-1.2 + -3.9x + 0.4x2 = 1.2 + 0.3x + -1.2 + -0.3x

Reorder the terms:
-1.2 + -3.9x + 0.4x2 = 1.2 + -1.2 + 0.3x + -0.3x

Combine like terms: 1.2 + -1.2 = 0.0
-1.2 + -3.9x + 0.4x2 = 0.0 + 0.3x + -0.3x
-1.2 + -3.9x + 0.4x2 = 0.3x + -0.3x

Combine like terms: 0.3x + -0.3x = 0.0
-1.2 + -3.9x + 0.4x2 = 0.0

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

Divide each side by '0.4'.
-3 + -9.75x + x2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -9.75x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + -9.75x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -9.75x + x2 = 0 + 3
-9.75x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
-9.75x + x2 = 3

The x term is -9.75x.  Take half its coefficient (-4.875).
Square it (23.765625) and add it to both sides.

Add '23.765625' to each side of the equation.
-9.75x + 23.765625 + x2 = 3 + 23.765625

Reorder the terms:
23.765625 + -9.75x + x2 = 3 + 23.765625

Combine like terms: 3 + 23.765625 = 26.765625
23.765625 + -9.75x + x2 = 26.765625

Factor a perfect square on the left side:
(x + -4.875)(x + -4.875) = 26.765625

Calculate the square root of the right side: 5.173550522

Break this problem into two subproblems by setting 
(x + -4.875) equal to 5.173550522 and -5.173550522.

Subproblem 1

x + -4.875 = 5.173550522 Simplifying x + -4.875 = 5.173550522 Reorder the terms: -4.875 + x = 5.173550522 Solving -4.875 + x = 5.173550522 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.875' to each side of the equation. -4.875 + 4.875 + x = 5.173550522 + 4.875 Combine like terms: -4.875 + 4.875 = 0.000 0.000 + x = 5.173550522 + 4.875 x = 5.173550522 + 4.875 Combine like terms: 5.173550522 + 4.875 = 10.048550522 x = 10.048550522 Simplifying x = 10.048550522

Subproblem 2

x + -4.875 = -5.173550522 Simplifying x + -4.875 = -5.173550522 Reorder the terms: -4.875 + x = -5.173550522 Solving -4.875 + x = -5.173550522 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.875' to each side of the equation. -4.875 + 4.875 + x = -5.173550522 + 4.875 Combine like terms: -4.875 + 4.875 = 0.000 0.000 + x = -5.173550522 + 4.875 x = -5.173550522 + 4.875 Combine like terms: -5.173550522 + 4.875 = -0.298550522 x = -0.298550522 Simplifying x = -0.298550522

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.048550522, -0.298550522}

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