x^2+4x=170

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Solution for x^2+4x=170 equation:


Simplifying
x2 + 4x = 170

Reorder the terms:
4x + x2 = 170

Solving
4x + x2 = 170

Solving for variable 'x'.

Reorder the terms:
-170 + 4x + x2 = 170 + -170

Combine like terms: 170 + -170 = 0
-170 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '170' to each side of the equation.
-170 + 4x + 170 + x2 = 0 + 170

Reorder the terms:
-170 + 170 + 4x + x2 = 0 + 170

Combine like terms: -170 + 170 = 0
0 + 4x + x2 = 0 + 170
4x + x2 = 0 + 170

Combine like terms: 0 + 170 = 170
4x + x2 = 170

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 170 + 4

Reorder the terms:
4 + 4x + x2 = 170 + 4

Combine like terms: 170 + 4 = 174
4 + 4x + x2 = 174

Factor a perfect square on the left side:
(x + 2)(x + 2) = 174

Calculate the square root of the right side: 13.190905958

Break this problem into two subproblems by setting 
(x + 2) equal to 13.190905958 and -13.190905958.

Subproblem 1

x + 2 = 13.190905958 Simplifying x + 2 = 13.190905958 Reorder the terms: 2 + x = 13.190905958 Solving 2 + x = 13.190905958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 13.190905958 + -2 Combine like terms: 2 + -2 = 0 0 + x = 13.190905958 + -2 x = 13.190905958 + -2 Combine like terms: 13.190905958 + -2 = 11.190905958 x = 11.190905958 Simplifying x = 11.190905958

Subproblem 2

x + 2 = -13.190905958 Simplifying x + 2 = -13.190905958 Reorder the terms: 2 + x = -13.190905958 Solving 2 + x = -13.190905958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -13.190905958 + -2 Combine like terms: 2 + -2 = 0 0 + x = -13.190905958 + -2 x = -13.190905958 + -2 Combine like terms: -13.190905958 + -2 = -15.190905958 x = -15.190905958 Simplifying x = -15.190905958

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.190905958, -15.190905958}

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