(x+1)(x+1)=60

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Solution for (x+1)(x+1)=60 equation:


Simplifying
(x + 1)(x + 1) = 60

Reorder the terms:
(1 + x)(x + 1) = 60

Reorder the terms:
(1 + x)(1 + x) = 60

Multiply (1 + x) * (1 + x)
(1(1 + x) + x(1 + x)) = 60
((1 * 1 + x * 1) + x(1 + x)) = 60
((1 + 1x) + x(1 + x)) = 60
(1 + 1x + (1 * x + x * x)) = 60
(1 + 1x + (1x + x2)) = 60

Combine like terms: 1x + 1x = 2x
(1 + 2x + x2) = 60

Solving
1 + 2x + x2 = 60

Solving for variable 'x'.

Reorder the terms:
1 + -60 + 2x + x2 = 60 + -60

Combine like terms: 1 + -60 = -59
-59 + 2x + x2 = 60 + -60

Combine like terms: 60 + -60 = 0
-59 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '59' to each side of the equation.
-59 + 2x + 59 + x2 = 0 + 59

Reorder the terms:
-59 + 59 + 2x + x2 = 0 + 59

Combine like terms: -59 + 59 = 0
0 + 2x + x2 = 0 + 59
2x + x2 = 0 + 59

Combine like terms: 0 + 59 = 59
2x + x2 = 59

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 = 59 + 1

Reorder the terms:
1 + 2x + x2 = 59 + 1

Combine like terms: 59 + 1 = 60
1 + 2x + x2 = 60

Factor a perfect square on the left side:
(x + 1)(x + 1) = 60

Calculate the square root of the right side: 7.745966692

Break this problem into two subproblems by setting 
(x + 1) equal to 7.745966692 and -7.745966692.

Subproblem 1

x + 1 = 7.745966692 Simplifying x + 1 = 7.745966692 Reorder the terms: 1 + x = 7.745966692 Solving 1 + x = 7.745966692 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 = 7.745966692 + -1 Combine like terms: 1 + -1 = 0 0 + x = 7.745966692 + -1 x = 7.745966692 + -1 Combine like terms: 7.745966692 + -1 = 6.745966692 x = 6.745966692 Simplifying x = 6.745966692

Subproblem 2

x + 1 = -7.745966692 Simplifying x + 1 = -7.745966692 Reorder the terms: 1 + x = -7.745966692 Solving 1 + x = -7.745966692 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 = -7.745966692 + -1 Combine like terms: 1 + -1 = 0 0 + x = -7.745966692 + -1 x = -7.745966692 + -1 Combine like terms: -7.745966692 + -1 = -8.745966692 x = -8.745966692 Simplifying x = -8.745966692

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.745966692, -8.745966692}

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