x(x+2)=89

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Solution for x(x+2)=89 equation:


Simplifying
x(x + 2) = 89

Reorder the terms:
x(2 + x) = 89
(2 * x + x * x) = 89
(2x + x2) = 89

Solving
2x + x2 = 89

Solving for variable 'x'.

Reorder the terms:
-89 + 2x + x2 = 89 + -89

Combine like terms: 89 + -89 = 0
-89 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '89' to each side of the equation.
-89 + 2x + 89 + x2 = 0 + 89

Reorder the terms:
-89 + 89 + 2x + x2 = 0 + 89

Combine like terms: -89 + 89 = 0
0 + 2x + x2 = 0 + 89
2x + x2 = 0 + 89

Combine like terms: 0 + 89 = 89
2x + x2 = 89

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 = 89 + 1

Reorder the terms:
1 + 2x + x2 = 89 + 1

Combine like terms: 89 + 1 = 90
1 + 2x + x2 = 90

Factor a perfect square on the left side:
(x + 1)(x + 1) = 90

Calculate the square root of the right side: 9.486832981

Break this problem into two subproblems by setting 
(x + 1) equal to 9.486832981 and -9.486832981.

Subproblem 1

x + 1 = 9.486832981 Simplifying x + 1 = 9.486832981 Reorder the terms: 1 + x = 9.486832981 Solving 1 + x = 9.486832981 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 = 9.486832981 + -1 Combine like terms: 1 + -1 = 0 0 + x = 9.486832981 + -1 x = 9.486832981 + -1 Combine like terms: 9.486832981 + -1 = 8.486832981 x = 8.486832981 Simplifying x = 8.486832981

Subproblem 2

x + 1 = -9.486832981 Simplifying x + 1 = -9.486832981 Reorder the terms: 1 + x = -9.486832981 Solving 1 + x = -9.486832981 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 = -9.486832981 + -1 Combine like terms: 1 + -1 = 0 0 + x = -9.486832981 + -1 x = -9.486832981 + -1 Combine like terms: -9.486832981 + -1 = -10.486832981 x = -10.486832981 Simplifying x = -10.486832981

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.486832981, -10.486832981}

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