(x+7)(x+8)=37

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Solution for (x+7)(x+8)=37 equation:


Simplifying
(x + 7)(x + 8) = 37

Reorder the terms:
(7 + x)(x + 8) = 37

Reorder the terms:
(7 + x)(8 + x) = 37

Multiply (7 + x) * (8 + x)
(7(8 + x) + x(8 + x)) = 37
((8 * 7 + x * 7) + x(8 + x)) = 37
((56 + 7x) + x(8 + x)) = 37
(56 + 7x + (8 * x + x * x)) = 37
(56 + 7x + (8x + x2)) = 37

Combine like terms: 7x + 8x = 15x
(56 + 15x + x2) = 37

Solving
56 + 15x + x2 = 37

Solving for variable 'x'.

Reorder the terms:
56 + -37 + 15x + x2 = 37 + -37

Combine like terms: 56 + -37 = 19
19 + 15x + x2 = 37 + -37

Combine like terms: 37 + -37 = 0
19 + 15x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-19' to each side of the equation.
19 + 15x + -19 + x2 = 0 + -19

Reorder the terms:
19 + -19 + 15x + x2 = 0 + -19

Combine like terms: 19 + -19 = 0
0 + 15x + x2 = 0 + -19
15x + x2 = 0 + -19

Combine like terms: 0 + -19 = -19
15x + x2 = -19

The x term is 15x.  Take half its coefficient (7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
15x + 56.25 + x2 = -19 + 56.25

Reorder the terms:
56.25 + 15x + x2 = -19 + 56.25

Combine like terms: -19 + 56.25 = 37.25
56.25 + 15x + x2 = 37.25

Factor a perfect square on the left side:
(x + 7.5)(x + 7.5) = 37.25

Calculate the square root of the right side: 6.103277808

Break this problem into two subproblems by setting 
(x + 7.5) equal to 6.103277808 and -6.103277808.

Subproblem 1

x + 7.5 = 6.103277808 Simplifying x + 7.5 = 6.103277808 Reorder the terms: 7.5 + x = 6.103277808 Solving 7.5 + x = 6.103277808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 6.103277808 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 6.103277808 + -7.5 x = 6.103277808 + -7.5 Combine like terms: 6.103277808 + -7.5 = -1.396722192 x = -1.396722192 Simplifying x = -1.396722192

Subproblem 2

x + 7.5 = -6.103277808 Simplifying x + 7.5 = -6.103277808 Reorder the terms: 7.5 + x = -6.103277808 Solving 7.5 + x = -6.103277808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -6.103277808 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -6.103277808 + -7.5 x = -6.103277808 + -7.5 Combine like terms: -6.103277808 + -7.5 = -13.603277808 x = -13.603277808 Simplifying x = -13.603277808

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.396722192, -13.603277808}

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