(x-0.7)(x+7)=

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Solution for (x-0.7)(x+7)= equation: 


Simplifying
(x + -0.7)(x + 7) = 0

Reorder the terms:
(-0.7 + x)(x + 7) = 0

Reorder the terms:
(-0.7 + x)(7 + x) = 0

Multiply (-0.7 + x) * (7 + x)
(-0.7(7 + x) + x(7 + x)) = 0
((7 * -0.7 + x * -0.7) + x(7 + x)) = 0
((-4.9 + -0.7x) + x(7 + x)) = 0
(-4.9 + -0.7x + (7 * x + x * x)) = 0
(-4.9 + -0.7x + (7x + x2)) = 0

Combine like terms: -0.7x + 7x = 6.3x
(-4.9 + 6.3x + x2) = 0

Solving
-4.9 + 6.3x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '4.9' to each side of the equation.
-4.9 + 6.3x + 4.9 + x2 = 0 + 4.9

Reorder the terms:
-4.9 + 4.9 + 6.3x + x2 = 0 + 4.9

Combine like terms: -4.9 + 4.9 = 0.0
0.0 + 6.3x + x2 = 0 + 4.9
6.3x + x2 = 0 + 4.9

Combine like terms: 0 + 4.9 = 4.9
6.3x + x2 = 4.9

The x term is 6.3x.  Take half its coefficient (3.15).
Square it (9.9225) and add it to both sides.

Add '9.9225' to each side of the equation.
6.3x + 9.9225 + x2 = 4.9 + 9.9225

Reorder the terms:
9.9225 + 6.3x + x2 = 4.9 + 9.9225

Combine like terms: 4.9 + 9.9225 = 14.8225
9.9225 + 6.3x + x2 = 14.8225

Factor a perfect square on the left side:
(x + 3.15)(x + 3.15) = 14.8225

Calculate the square root of the right side: 3.85

Break this problem into two subproblems by setting 
(x + 3.15) equal to 3.85 and -3.85.


Subproblem 1
x + 3.15 = 3.85

Simplifying
x + 3.15 = 3.85

Reorder the terms:
3.15 + x = 3.85

Solving
3.15 + x = 3.85

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3.15' to each side of the equation.
3.15 + -3.15 + x = 3.85 + -3.15

Combine like terms: 3.15 + -3.15 = 0.00
0.00 + x = 3.85 + -3.15
x = 3.85 + -3.15

Combine like terms: 3.85 + -3.15 = 0.7
x = 0.7

Simplifying
x = 0.7


Subproblem 2
x + 3.15 = -3.85

Simplifying
x + 3.15 = -3.85

Reorder the terms:
3.15 + x = -3.85

Solving
3.15 + x = -3.85

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3.15' to each side of the equation.
3.15 + -3.15 + x = -3.85 + -3.15

Combine like terms: 3.15 + -3.15 = 0.00
0.00 + x = -3.85 + -3.15
x = -3.85 + -3.15

Combine like terms: -3.85 + -3.15 = -7
x = -7

Simplifying
x = -7


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.7, -7}

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