529=24x+x^2

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Solution for 529=24x+x^2 equation:


Simplifying
529 = 24x + x2

Solving
529 = 24x + x2

Solving for variable 'x'.

Reorder the terms:
529 + -24x + -1x2 = 24x + -24x + x2 + -1x2

Combine like terms: 24x + -24x = 0
529 + -24x + -1x2 = 0 + x2 + -1x2
529 + -24x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
529 + -24x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-529 + 24x + x2 = 0

Move the constant term to the right:

Add '529' to each side of the equation.
-529 + 24x + 529 + x2 = 0 + 529

Reorder the terms:
-529 + 529 + 24x + x2 = 0 + 529

Combine like terms: -529 + 529 = 0
0 + 24x + x2 = 0 + 529
24x + x2 = 0 + 529

Combine like terms: 0 + 529 = 529
24x + x2 = 529

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 = 529 + 144

Reorder the terms:
144 + 24x + x2 = 529 + 144

Combine like terms: 529 + 144 = 673
144 + 24x + x2 = 673

Factor a perfect square on the left side:
(x + 12)(x + 12) = 673

Calculate the square root of the right side: 25.942243542

Break this problem into two subproblems by setting 
(x + 12) equal to 25.942243542 and -25.942243542.

Subproblem 1

x + 12 = 25.942243542 Simplifying x + 12 = 25.942243542 Reorder the terms: 12 + x = 25.942243542 Solving 12 + x = 25.942243542 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 = 25.942243542 + -12 Combine like terms: 12 + -12 = 0 0 + x = 25.942243542 + -12 x = 25.942243542 + -12 Combine like terms: 25.942243542 + -12 = 13.942243542 x = 13.942243542 Simplifying x = 13.942243542

Subproblem 2

x + 12 = -25.942243542 Simplifying x + 12 = -25.942243542 Reorder the terms: 12 + x = -25.942243542 Solving 12 + x = -25.942243542 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 = -25.942243542 + -12 Combine like terms: 12 + -12 = 0 0 + x = -25.942243542 + -12 x = -25.942243542 + -12 Combine like terms: -25.942243542 + -12 = -37.942243542 x = -37.942243542 Simplifying x = -37.942243542

Solution

The solution to the problem is based on the solutions from the subproblems. x = {13.942243542, -37.942243542}

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