(x+1)(x+1)-5x+10=3x+7

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Solution for (x+1)(x+1)-5x+10=3x+7 equation:


Simplifying
(x + 1)(x + 1) + -5x + 10 = 3x + 7

Reorder the terms:
(1 + x)(x + 1) + -5x + 10 = 3x + 7

Reorder the terms:
(1 + x)(1 + x) + -5x + 10 = 3x + 7

Multiply (1 + x) * (1 + x)
(1(1 + x) + x(1 + x)) + -5x + 10 = 3x + 7
((1 * 1 + x * 1) + x(1 + x)) + -5x + 10 = 3x + 7
((1 + 1x) + x(1 + x)) + -5x + 10 = 3x + 7
(1 + 1x + (1 * x + x * x)) + -5x + 10 = 3x + 7
(1 + 1x + (1x + x2)) + -5x + 10 = 3x + 7

Combine like terms: 1x + 1x = 2x
(1 + 2x + x2) + -5x + 10 = 3x + 7

Reorder the terms:
1 + 10 + 2x + -5x + x2 = 3x + 7

Combine like terms: 1 + 10 = 11
11 + 2x + -5x + x2 = 3x + 7

Combine like terms: 2x + -5x = -3x
11 + -3x + x2 = 3x + 7

Reorder the terms:
11 + -3x + x2 = 7 + 3x

Solving
11 + -3x + x2 = 7 + 3x

Solving for variable 'x'.

Reorder the terms:
11 + -7 + -3x + -3x + x2 = 7 + 3x + -7 + -3x

Combine like terms: 11 + -7 = 4
4 + -3x + -3x + x2 = 7 + 3x + -7 + -3x

Combine like terms: -3x + -3x = -6x
4 + -6x + x2 = 7 + 3x + -7 + -3x

Reorder the terms:
4 + -6x + x2 = 7 + -7 + 3x + -3x

Combine like terms: 7 + -7 = 0
4 + -6x + x2 = 0 + 3x + -3x
4 + -6x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
4 + -6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -6x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + -6x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -6x + x2 = 0 + -4
-6x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-6x + x2 = -4

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = -4 + 9

Reorder the terms:
9 + -6x + x2 = -4 + 9

Combine like terms: -4 + 9 = 5
9 + -6x + x2 = 5

Factor a perfect square on the left side:
(x + -3)(x + -3) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(x + -3) equal to 2.236067978 and -2.236067978.

Subproblem 1

x + -3 = 2.236067978 Simplifying x + -3 = 2.236067978 Reorder the terms: -3 + x = 2.236067978 Solving -3 + x = 2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 2.236067978 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.236067978 + 3 x = 2.236067978 + 3 Combine like terms: 2.236067978 + 3 = 5.236067978 x = 5.236067978 Simplifying x = 5.236067978

Subproblem 2

x + -3 = -2.236067978 Simplifying x + -3 = -2.236067978 Reorder the terms: -3 + x = -2.236067978 Solving -3 + x = -2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -2.236067978 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.236067978 + 3 x = -2.236067978 + 3 Combine like terms: -2.236067978 + 3 = 0.763932022 x = 0.763932022 Simplifying x = 0.763932022

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.236067978, 0.763932022}

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