x^2-170+24x=0

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Solution for x^2-170+24x=0 equation:


Simplifying
x2 + -170 + 24x = 0

Reorder the terms:
-170 + 24x + x2 = 0

Solving
-170 + 24x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '170' to each side of the equation.
-170 + 24x + 170 + x2 = 0 + 170

Reorder the terms:
-170 + 170 + 24x + x2 = 0 + 170

Combine like terms: -170 + 170 = 0
0 + 24x + x2 = 0 + 170
24x + x2 = 0 + 170

Combine like terms: 0 + 170 = 170
24x + x2 = 170

The x term is 24x.  Take half its coefficient (12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
24x + 144 + x2 = 170 + 144

Reorder the terms:
144 + 24x + x2 = 170 + 144

Combine like terms: 170 + 144 = 314
144 + 24x + x2 = 314

Factor a perfect square on the left side:
(x + 12)(x + 12) = 314

Calculate the square root of the right side: 17.720045147

Break this problem into two subproblems by setting 
(x + 12) equal to 17.720045147 and -17.720045147.

Subproblem 1

x + 12 = 17.720045147 Simplifying x + 12 = 17.720045147 Reorder the terms: 12 + x = 17.720045147 Solving 12 + x = 17.720045147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 17.720045147 + -12 Combine like terms: 12 + -12 = 0 0 + x = 17.720045147 + -12 x = 17.720045147 + -12 Combine like terms: 17.720045147 + -12 = 5.720045147 x = 5.720045147 Simplifying x = 5.720045147

Subproblem 2

x + 12 = -17.720045147 Simplifying x + 12 = -17.720045147 Reorder the terms: 12 + x = -17.720045147 Solving 12 + x = -17.720045147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = -17.720045147 + -12 Combine like terms: 12 + -12 = 0 0 + x = -17.720045147 + -12 x = -17.720045147 + -12 Combine like terms: -17.720045147 + -12 = -29.720045147 x = -29.720045147 Simplifying x = -29.720045147

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.720045147, -29.720045147}

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