(x+7)(x+5)=70

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Solution for (x+7)(x+5)=70 equation:


Simplifying
(x + 7)(x + 5) = 70

Reorder the terms:
(7 + x)(x + 5) = 70

Reorder the terms:
(7 + x)(5 + x) = 70

Multiply (7 + x) * (5 + x)
(7(5 + x) + x(5 + x)) = 70
((5 * 7 + x * 7) + x(5 + x)) = 70
((35 + 7x) + x(5 + x)) = 70
(35 + 7x + (5 * x + x * x)) = 70
(35 + 7x + (5x + x2)) = 70

Combine like terms: 7x + 5x = 12x
(35 + 12x + x2) = 70

Solving
35 + 12x + x2 = 70

Solving for variable 'x'.

Reorder the terms:
35 + -70 + 12x + x2 = 70 + -70

Combine like terms: 35 + -70 = -35
-35 + 12x + x2 = 70 + -70

Combine like terms: 70 + -70 = 0
-35 + 12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '35' to each side of the equation.
-35 + 12x + 35 + x2 = 0 + 35

Reorder the terms:
-35 + 35 + 12x + x2 = 0 + 35

Combine like terms: -35 + 35 = 0
0 + 12x + x2 = 0 + 35
12x + x2 = 0 + 35

Combine like terms: 0 + 35 = 35
12x + x2 = 35

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = 35 + 36

Reorder the terms:
36 + 12x + x2 = 35 + 36

Combine like terms: 35 + 36 = 71
36 + 12x + x2 = 71

Factor a perfect square on the left side:
(x + 6)(x + 6) = 71

Calculate the square root of the right side: 8.426149773

Break this problem into two subproblems by setting 
(x + 6) equal to 8.426149773 and -8.426149773.

Subproblem 1

x + 6 = 8.426149773 Simplifying x + 6 = 8.426149773 Reorder the terms: 6 + x = 8.426149773 Solving 6 + x = 8.426149773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 8.426149773 + -6 Combine like terms: 6 + -6 = 0 0 + x = 8.426149773 + -6 x = 8.426149773 + -6 Combine like terms: 8.426149773 + -6 = 2.426149773 x = 2.426149773 Simplifying x = 2.426149773

Subproblem 2

x + 6 = -8.426149773 Simplifying x + 6 = -8.426149773 Reorder the terms: 6 + x = -8.426149773 Solving 6 + x = -8.426149773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -8.426149773 + -6 Combine like terms: 6 + -6 = 0 0 + x = -8.426149773 + -6 x = -8.426149773 + -6 Combine like terms: -8.426149773 + -6 = -14.426149773 x = -14.426149773 Simplifying x = -14.426149773

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.426149773, -14.426149773}

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