(3+x)(3+x)=160

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Solution for (3+x)(3+x)=160 equation:


Simplifying
(3 + x)(3 + x) = 160

Multiply (3 + x) * (3 + x)
(3(3 + x) + x(3 + x)) = 160
((3 * 3 + x * 3) + x(3 + x)) = 160
((9 + 3x) + x(3 + x)) = 160
(9 + 3x + (3 * x + x * x)) = 160
(9 + 3x + (3x + x2)) = 160

Combine like terms: 3x + 3x = 6x
(9 + 6x + x2) = 160

Solving
9 + 6x + x2 = 160

Solving for variable 'x'.

Reorder the terms:
9 + -160 + 6x + x2 = 160 + -160

Combine like terms: 9 + -160 = -151
-151 + 6x + x2 = 160 + -160

Combine like terms: 160 + -160 = 0
-151 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '151' to each side of the equation.
-151 + 6x + 151 + x2 = 0 + 151

Reorder the terms:
-151 + 151 + 6x + x2 = 0 + 151

Combine like terms: -151 + 151 = 0
0 + 6x + x2 = 0 + 151
6x + x2 = 0 + 151

Combine like terms: 0 + 151 = 151
6x + x2 = 151

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 = 151 + 9

Reorder the terms:
9 + 6x + x2 = 151 + 9

Combine like terms: 151 + 9 = 160
9 + 6x + x2 = 160

Factor a perfect square on the left side:
(x + 3)(x + 3) = 160

Calculate the square root of the right side: 12.649110641

Break this problem into two subproblems by setting 
(x + 3) equal to 12.649110641 and -12.649110641.

Subproblem 1

x + 3 = 12.649110641 Simplifying x + 3 = 12.649110641 Reorder the terms: 3 + x = 12.649110641 Solving 3 + x = 12.649110641 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 = 12.649110641 + -3 Combine like terms: 3 + -3 = 0 0 + x = 12.649110641 + -3 x = 12.649110641 + -3 Combine like terms: 12.649110641 + -3 = 9.649110641 x = 9.649110641 Simplifying x = 9.649110641

Subproblem 2

x + 3 = -12.649110641 Simplifying x + 3 = -12.649110641 Reorder the terms: 3 + x = -12.649110641 Solving 3 + x = -12.649110641 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 = -12.649110641 + -3 Combine like terms: 3 + -3 = 0 0 + x = -12.649110641 + -3 x = -12.649110641 + -3 Combine like terms: -12.649110641 + -3 = -15.649110641 x = -15.649110641 Simplifying x = -15.649110641

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.649110641, -15.649110641}

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