(x*x)+x=170

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Solution for (x*x)+x=170 equation:


Simplifying
(x * x) + x = 170

Multiply x * x
(x2) + x = 170
x2 + x = 170

Reorder the terms:
x + x2 = 170

Solving
x + x2 = 170

Solving for variable 'x'.

Reorder the terms:
-170 + x + x2 = 170 + -170

Combine like terms: 170 + -170 = 0
-170 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '170' to each side of the equation.
-170 + x + 170 + x2 = 0 + 170

Reorder the terms:
-170 + 170 + x + x2 = 0 + 170

Combine like terms: -170 + 170 = 0
0 + x + x2 = 0 + 170
x + x2 = 0 + 170

Combine like terms: 0 + 170 = 170
x + x2 = 170

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = 170 + 0.25

Reorder the terms:
0.25 + x + x2 = 170 + 0.25

Combine like terms: 170 + 0.25 = 170.25
0.25 + x + x2 = 170.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 170.25

Calculate the square root of the right side: 13.047988351

Break this problem into two subproblems by setting 
(x + 0.5) equal to 13.047988351 and -13.047988351.

Subproblem 1

x + 0.5 = 13.047988351 Simplifying x + 0.5 = 13.047988351 Reorder the terms: 0.5 + x = 13.047988351 Solving 0.5 + x = 13.047988351 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 13.047988351 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 13.047988351 + -0.5 x = 13.047988351 + -0.5 Combine like terms: 13.047988351 + -0.5 = 12.547988351 x = 12.547988351 Simplifying x = 12.547988351

Subproblem 2

x + 0.5 = -13.047988351 Simplifying x + 0.5 = -13.047988351 Reorder the terms: 0.5 + x = -13.047988351 Solving 0.5 + x = -13.047988351 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -13.047988351 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -13.047988351 + -0.5 x = -13.047988351 + -0.5 Combine like terms: -13.047988351 + -0.5 = -13.547988351 x = -13.547988351 Simplifying x = -13.547988351

Solution

The solution to the problem is based on the solutions from the subproblems. x = {12.547988351, -13.547988351}

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