(x-1)(x+1)+13=10x

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Solution for (x-1)(x+1)+13=10x equation:


Simplifying
(x + -1)(x + 1) + 13 = 10x

Reorder the terms:
(-1 + x)(x + 1) + 13 = 10x

Reorder the terms:
(-1 + x)(1 + x) + 13 = 10x

Multiply (-1 + x) * (1 + x)
(-1(1 + x) + x(1 + x)) + 13 = 10x
((1 * -1 + x * -1) + x(1 + x)) + 13 = 10x
((-1 + -1x) + x(1 + x)) + 13 = 10x
(-1 + -1x + (1 * x + x * x)) + 13 = 10x
(-1 + -1x + (1x + x2)) + 13 = 10x

Combine like terms: -1x + 1x = 0
(-1 + 0 + x2) + 13 = 10x
(-1 + x2) + 13 = 10x

Reorder the terms:
-1 + 13 + x2 = 10x

Combine like terms: -1 + 13 = 12
12 + x2 = 10x

Solving
12 + x2 = 10x

Solving for variable 'x'.

Reorder the terms:
12 + -10x + x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
12 + -10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-12' to each side of the equation.
12 + -10x + -12 + x2 = 0 + -12

Reorder the terms:
12 + -12 + -10x + x2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -10x + x2 = 0 + -12
-10x + x2 = 0 + -12

Combine like terms: 0 + -12 = -12
-10x + x2 = -12

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = -12 + 25

Reorder the terms:
25 + -10x + x2 = -12 + 25

Combine like terms: -12 + 25 = 13
25 + -10x + x2 = 13

Factor a perfect square on the left side:
(x + -5)(x + -5) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(x + -5) equal to 3.605551275 and -3.605551275.

Subproblem 1

x + -5 = 3.605551275 Simplifying x + -5 = 3.605551275 Reorder the terms: -5 + x = 3.605551275 Solving -5 + x = 3.605551275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 3.605551275 + 5 Combine like terms: -5 + 5 = 0 0 + x = 3.605551275 + 5 x = 3.605551275 + 5 Combine like terms: 3.605551275 + 5 = 8.605551275 x = 8.605551275 Simplifying x = 8.605551275

Subproblem 2

x + -5 = -3.605551275 Simplifying x + -5 = -3.605551275 Reorder the terms: -5 + x = -3.605551275 Solving -5 + x = -3.605551275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -3.605551275 + 5 Combine like terms: -5 + 5 = 0 0 + x = -3.605551275 + 5 x = -3.605551275 + 5 Combine like terms: -3.605551275 + 5 = 1.394448725 x = 1.394448725 Simplifying x = 1.394448725

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.605551275, 1.394448725}

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