x^2+24x=17

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Solution for x^2+24x=17 equation:


Simplifying
x2 + 24x = 17

Reorder the terms:
24x + x2 = 17

Solving
24x + x2 = 17

Solving for variable 'x'.

Reorder the terms:
-17 + 24x + x2 = 17 + -17

Combine like terms: 17 + -17 = 0
-17 + 24x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '17' to each side of the equation.
-17 + 24x + 17 + x2 = 0 + 17

Reorder the terms:
-17 + 17 + 24x + x2 = 0 + 17

Combine like terms: -17 + 17 = 0
0 + 24x + x2 = 0 + 17
24x + x2 = 0 + 17

Combine like terms: 0 + 17 = 17
24x + x2 = 17

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 = 17 + 144

Reorder the terms:
144 + 24x + x2 = 17 + 144

Combine like terms: 17 + 144 = 161
144 + 24x + x2 = 161

Factor a perfect square on the left side:
(x + 12)(x + 12) = 161

Calculate the square root of the right side: 12.68857754

Break this problem into two subproblems by setting 
(x + 12) equal to 12.68857754 and -12.68857754.

Subproblem 1

x + 12 = 12.68857754 Simplifying x + 12 = 12.68857754 Reorder the terms: 12 + x = 12.68857754 Solving 12 + x = 12.68857754 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 = 12.68857754 + -12 Combine like terms: 12 + -12 = 0 0 + x = 12.68857754 + -12 x = 12.68857754 + -12 Combine like terms: 12.68857754 + -12 = 0.68857754 x = 0.68857754 Simplifying x = 0.68857754

Subproblem 2

x + 12 = -12.68857754 Simplifying x + 12 = -12.68857754 Reorder the terms: 12 + x = -12.68857754 Solving 12 + x = -12.68857754 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 = -12.68857754 + -12 Combine like terms: 12 + -12 = 0 0 + x = -12.68857754 + -12 x = -12.68857754 + -12 Combine like terms: -12.68857754 + -12 = -24.68857754 x = -24.68857754 Simplifying x = -24.68857754

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.68857754, -24.68857754}

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