4(x+1.2)(x-8)=20

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Solution for 4(x+1.2)(x-8)=20 equation:


Simplifying
4(x + 1.2)(x + -8) = 20

Reorder the terms:
4(1.2 + x)(x + -8) = 20

Reorder the terms:
4(1.2 + x)(-8 + x) = 20

Multiply (1.2 + x) * (-8 + x)
4(1.2(-8 + x) + x(-8 + x)) = 20
4((-8 * 1.2 + x * 1.2) + x(-8 + x)) = 20
4((-9.6 + 1.2x) + x(-8 + x)) = 20
4(-9.6 + 1.2x + (-8 * x + x * x)) = 20
4(-9.6 + 1.2x + (-8x + x2)) = 20

Combine like terms: 1.2x + -8x = -6.8x
4(-9.6 + -6.8x + x2) = 20
(-9.6 * 4 + -6.8x * 4 + x2 * 4) = 20
(-38.4 + -27.2x + 4x2) = 20

Solving
-38.4 + -27.2x + 4x2 = 20

Solving for variable 'x'.

Reorder the terms:
-38.4 + -20 + -27.2x + 4x2 = 20 + -20

Combine like terms: -38.4 + -20 = -58.4
-58.4 + -27.2x + 4x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-58.4 + -27.2x + 4x2 = 0

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

Divide each side by '4'.
-14.6 + -6.8x + x2 = 0

Move the constant term to the right:

Add '14.6' to each side of the equation.
-14.6 + -6.8x + 14.6 + x2 = 0 + 14.6

Reorder the terms:
-14.6 + 14.6 + -6.8x + x2 = 0 + 14.6

Combine like terms: -14.6 + 14.6 = 0.0
0.0 + -6.8x + x2 = 0 + 14.6
-6.8x + x2 = 0 + 14.6

Combine like terms: 0 + 14.6 = 14.6
-6.8x + x2 = 14.6

The x term is -6.8x.  Take half its coefficient (-3.4).
Square it (11.56) and add it to both sides.

Add '11.56' to each side of the equation.
-6.8x + 11.56 + x2 = 14.6 + 11.56

Reorder the terms:
11.56 + -6.8x + x2 = 14.6 + 11.56

Combine like terms: 14.6 + 11.56 = 26.16
11.56 + -6.8x + x2 = 26.16

Factor a perfect square on the left side:
(x + -3.4)(x + -3.4) = 26.16

Calculate the square root of the right side: 5.114684741

Break this problem into two subproblems by setting 
(x + -3.4) equal to 5.114684741 and -5.114684741.

Subproblem 1

x + -3.4 = 5.114684741 Simplifying x + -3.4 = 5.114684741 Reorder the terms: -3.4 + x = 5.114684741 Solving -3.4 + x = 5.114684741 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.4' to each side of the equation. -3.4 + 3.4 + x = 5.114684741 + 3.4 Combine like terms: -3.4 + 3.4 = 0.0 0.0 + x = 5.114684741 + 3.4 x = 5.114684741 + 3.4 Combine like terms: 5.114684741 + 3.4 = 8.514684741 x = 8.514684741 Simplifying x = 8.514684741

Subproblem 2

x + -3.4 = -5.114684741 Simplifying x + -3.4 = -5.114684741 Reorder the terms: -3.4 + x = -5.114684741 Solving -3.4 + x = -5.114684741 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.4' to each side of the equation. -3.4 + 3.4 + x = -5.114684741 + 3.4 Combine like terms: -3.4 + 3.4 = 0.0 0.0 + x = -5.114684741 + 3.4 x = -5.114684741 + 3.4 Combine like terms: -5.114684741 + 3.4 = -1.714684741 x = -1.714684741 Simplifying x = -1.714684741

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.514684741, -1.714684741}

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