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

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


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

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

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

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

Combine like terms: -1x + -1x = -2x
(1 + -2x + x2) = 10

Solving
1 + -2x + x2 = 10

Solving for variable 'x'.

Reorder the terms:
1 + -10 + -2x + x2 = 10 + -10

Combine like terms: 1 + -10 = -9
-9 + -2x + x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-9 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -2x + 9 + x2 = 0 + 9

Reorder the terms:
-9 + 9 + -2x + x2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2x + x2 = 0 + 9
-2x + x2 = 0 + 9

Combine like terms: 0 + 9 = 9
-2x + x2 = 9

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 = 9 + 1

Reorder the terms:
1 + -2x + x2 = 9 + 1

Combine like terms: 9 + 1 = 10
1 + -2x + x2 = 10

Factor a perfect square on the left side:
(x + -1)(x + -1) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(x + -1) equal to 3.16227766 and -3.16227766.

Subproblem 1

x + -1 = 3.16227766 Simplifying x + -1 = 3.16227766 Reorder the terms: -1 + x = 3.16227766 Solving -1 + x = 3.16227766 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 = 3.16227766 + 1 Combine like terms: -1 + 1 = 0 0 + x = 3.16227766 + 1 x = 3.16227766 + 1 Combine like terms: 3.16227766 + 1 = 4.16227766 x = 4.16227766 Simplifying x = 4.16227766

Subproblem 2

x + -1 = -3.16227766 Simplifying x + -1 = -3.16227766 Reorder the terms: -1 + x = -3.16227766 Solving -1 + x = -3.16227766 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 = -3.16227766 + 1 Combine like terms: -1 + 1 = 0 0 + x = -3.16227766 + 1 x = -3.16227766 + 1 Combine like terms: -3.16227766 + 1 = -2.16227766 x = -2.16227766 Simplifying x = -2.16227766

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.16227766, -2.16227766}

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