x^2+42x-432=0

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Solution for x^2+42x-432=0 equation:


Simplifying
x2 + 42x + -432 = 0

Reorder the terms:
-432 + 42x + x2 = 0

Solving
-432 + 42x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '432' to each side of the equation.
-432 + 42x + 432 + x2 = 0 + 432

Reorder the terms:
-432 + 432 + 42x + x2 = 0 + 432

Combine like terms: -432 + 432 = 0
0 + 42x + x2 = 0 + 432
42x + x2 = 0 + 432

Combine like terms: 0 + 432 = 432
42x + x2 = 432

The x term is 42x.  Take half its coefficient (21).
Square it (441) and add it to both sides.

Add '441' to each side of the equation.
42x + 441 + x2 = 432 + 441

Reorder the terms:
441 + 42x + x2 = 432 + 441

Combine like terms: 432 + 441 = 873
441 + 42x + x2 = 873

Factor a perfect square on the left side:
(x + 21)(x + 21) = 873

Calculate the square root of the right side: 29.546573405

Break this problem into two subproblems by setting 
(x + 21) equal to 29.546573405 and -29.546573405.

Subproblem 1

x + 21 = 29.546573405 Simplifying x + 21 = 29.546573405 Reorder the terms: 21 + x = 29.546573405 Solving 21 + x = 29.546573405 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + x = 29.546573405 + -21 Combine like terms: 21 + -21 = 0 0 + x = 29.546573405 + -21 x = 29.546573405 + -21 Combine like terms: 29.546573405 + -21 = 8.546573405 x = 8.546573405 Simplifying x = 8.546573405

Subproblem 2

x + 21 = -29.546573405 Simplifying x + 21 = -29.546573405 Reorder the terms: 21 + x = -29.546573405 Solving 21 + x = -29.546573405 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + x = -29.546573405 + -21 Combine like terms: 21 + -21 = 0 0 + x = -29.546573405 + -21 x = -29.546573405 + -21 Combine like terms: -29.546573405 + -21 = -50.546573405 x = -50.546573405 Simplifying x = -50.546573405

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.546573405, -50.546573405}

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