(x+7)(x-9)=25

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Solution for (x+7)(x-9)=25 equation:


Simplifying
(x + 7)(x + -9) = 25

Reorder the terms:
(7 + x)(x + -9) = 25

Reorder the terms:
(7 + x)(-9 + x) = 25

Multiply (7 + x) * (-9 + x)
(7(-9 + x) + x(-9 + x)) = 25
((-9 * 7 + x * 7) + x(-9 + x)) = 25
((-63 + 7x) + x(-9 + x)) = 25
(-63 + 7x + (-9 * x + x * x)) = 25
(-63 + 7x + (-9x + x2)) = 25

Combine like terms: 7x + -9x = -2x
(-63 + -2x + x2) = 25

Solving
-63 + -2x + x2 = 25

Solving for variable 'x'.

Reorder the terms:
-63 + -25 + -2x + x2 = 25 + -25

Combine like terms: -63 + -25 = -88
-88 + -2x + x2 = 25 + -25

Combine like terms: 25 + -25 = 0
-88 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '88' to each side of the equation.
-88 + -2x + 88 + x2 = 0 + 88

Reorder the terms:
-88 + 88 + -2x + x2 = 0 + 88

Combine like terms: -88 + 88 = 0
0 + -2x + x2 = 0 + 88
-2x + x2 = 0 + 88

Combine like terms: 0 + 88 = 88
-2x + x2 = 88

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 88 + 1

Reorder the terms:
1 + -2x + x2 = 88 + 1

Combine like terms: 88 + 1 = 89
1 + -2x + x2 = 89

Factor a perfect square on the left side:
(x + -1)(x + -1) = 89

Calculate the square root of the right side: 9.433981132

Break this problem into two subproblems by setting 
(x + -1) equal to 9.433981132 and -9.433981132.

Subproblem 1

x + -1 = 9.433981132 Simplifying x + -1 = 9.433981132 Reorder the terms: -1 + x = 9.433981132 Solving -1 + x = 9.433981132 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 9.433981132 + 1 Combine like terms: -1 + 1 = 0 0 + x = 9.433981132 + 1 x = 9.433981132 + 1 Combine like terms: 9.433981132 + 1 = 10.433981132 x = 10.433981132 Simplifying x = 10.433981132

Subproblem 2

x + -1 = -9.433981132 Simplifying x + -1 = -9.433981132 Reorder the terms: -1 + x = -9.433981132 Solving -1 + x = -9.433981132 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -9.433981132 + 1 Combine like terms: -1 + 1 = 0 0 + x = -9.433981132 + 1 x = -9.433981132 + 1 Combine like terms: -9.433981132 + 1 = -8.433981132 x = -8.433981132 Simplifying x = -8.433981132

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.433981132, -8.433981132}

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