x^2+21x=378

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Solution for x^2+21x=378 equation:


Simplifying
x2 + 21x = 378

Reorder the terms:
21x + x2 = 378

Solving
21x + x2 = 378

Solving for variable 'x'.

Reorder the terms:
-378 + 21x + x2 = 378 + -378

Combine like terms: 378 + -378 = 0
-378 + 21x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '378' to each side of the equation.
-378 + 21x + 378 + x2 = 0 + 378

Reorder the terms:
-378 + 378 + 21x + x2 = 0 + 378

Combine like terms: -378 + 378 = 0
0 + 21x + x2 = 0 + 378
21x + x2 = 0 + 378

Combine like terms: 0 + 378 = 378
21x + x2 = 378

The x term is 21x.  Take half its coefficient (10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
21x + 110.25 + x2 = 378 + 110.25

Reorder the terms:
110.25 + 21x + x2 = 378 + 110.25

Combine like terms: 378 + 110.25 = 488.25
110.25 + 21x + x2 = 488.25

Factor a perfect square on the left side:
(x + 10.5)(x + 10.5) = 488.25

Calculate the square root of the right side: 22.096379794

Break this problem into two subproblems by setting 
(x + 10.5) equal to 22.096379794 and -22.096379794.

Subproblem 1

x + 10.5 = 22.096379794 Simplifying x + 10.5 = 22.096379794 Reorder the terms: 10.5 + x = 22.096379794 Solving 10.5 + x = 22.096379794 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + x = 22.096379794 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = 22.096379794 + -10.5 x = 22.096379794 + -10.5 Combine like terms: 22.096379794 + -10.5 = 11.596379794 x = 11.596379794 Simplifying x = 11.596379794

Subproblem 2

x + 10.5 = -22.096379794 Simplifying x + 10.5 = -22.096379794 Reorder the terms: 10.5 + x = -22.096379794 Solving 10.5 + x = -22.096379794 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + x = -22.096379794 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = -22.096379794 + -10.5 x = -22.096379794 + -10.5 Combine like terms: -22.096379794 + -10.5 = -32.596379794 x = -32.596379794 Simplifying x = -32.596379794

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.596379794, -32.596379794}

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