(7x+4)(5x+8)=144

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Solution for (7x+4)(5x+8)=144 equation:


Simplifying
(7x + 4)(5x + 8) = 144

Reorder the terms:
(4 + 7x)(5x + 8) = 144

Reorder the terms:
(4 + 7x)(8 + 5x) = 144

Multiply (4 + 7x) * (8 + 5x)
(4(8 + 5x) + 7x * (8 + 5x)) = 144
((8 * 4 + 5x * 4) + 7x * (8 + 5x)) = 144
((32 + 20x) + 7x * (8 + 5x)) = 144
(32 + 20x + (8 * 7x + 5x * 7x)) = 144
(32 + 20x + (56x + 35x2)) = 144

Combine like terms: 20x + 56x = 76x
(32 + 76x + 35x2) = 144

Solving
32 + 76x + 35x2 = 144

Solving for variable 'x'.

Reorder the terms:
32 + -144 + 76x + 35x2 = 144 + -144

Combine like terms: 32 + -144 = -112
-112 + 76x + 35x2 = 144 + -144

Combine like terms: 144 + -144 = 0
-112 + 76x + 35x2 = 0

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

Divide each side by '35'.
-3.2 + 2.171428571x + x2 = 0

Move the constant term to the right:

Add '3.2' to each side of the equation.
-3.2 + 2.171428571x + 3.2 + x2 = 0 + 3.2

Reorder the terms:
-3.2 + 3.2 + 2.171428571x + x2 = 0 + 3.2

Combine like terms: -3.2 + 3.2 = 0.0
0.0 + 2.171428571x + x2 = 0 + 3.2
2.171428571x + x2 = 0 + 3.2

Combine like terms: 0 + 3.2 = 3.2
2.171428571x + x2 = 3.2

The x term is 2.171428571x.  Take half its coefficient (1.085714286).
Square it (1.178775511) and add it to both sides.

Add '1.178775511' to each side of the equation.
2.171428571x + 1.178775511 + x2 = 3.2 + 1.178775511

Reorder the terms:
1.178775511 + 2.171428571x + x2 = 3.2 + 1.178775511

Combine like terms: 3.2 + 1.178775511 = 4.378775511
1.178775511 + 2.171428571x + x2 = 4.378775511

Factor a perfect square on the left side:
(x + 1.085714286)(x + 1.085714286) = 4.378775511

Calculate the square root of the right side: 2.092552391

Break this problem into two subproblems by setting 
(x + 1.085714286) equal to 2.092552391 and -2.092552391.

Subproblem 1

x + 1.085714286 = 2.092552391 Simplifying x + 1.085714286 = 2.092552391 Reorder the terms: 1.085714286 + x = 2.092552391 Solving 1.085714286 + x = 2.092552391 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.085714286' to each side of the equation. 1.085714286 + -1.085714286 + x = 2.092552391 + -1.085714286 Combine like terms: 1.085714286 + -1.085714286 = 0.000000000 0.000000000 + x = 2.092552391 + -1.085714286 x = 2.092552391 + -1.085714286 Combine like terms: 2.092552391 + -1.085714286 = 1.006838105 x = 1.006838105 Simplifying x = 1.006838105

Subproblem 2

x + 1.085714286 = -2.092552391 Simplifying x + 1.085714286 = -2.092552391 Reorder the terms: 1.085714286 + x = -2.092552391 Solving 1.085714286 + x = -2.092552391 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.085714286' to each side of the equation. 1.085714286 + -1.085714286 + x = -2.092552391 + -1.085714286 Combine like terms: 1.085714286 + -1.085714286 = 0.000000000 0.000000000 + x = -2.092552391 + -1.085714286 x = -2.092552391 + -1.085714286 Combine like terms: -2.092552391 + -1.085714286 = -3.178266677 x = -3.178266677 Simplifying x = -3.178266677

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.006838105, -3.178266677}

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