21x+x^2=48

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Solution for 21x+x^2=48 equation:


Simplifying
21x + x2 = 48

Solving
21x + x2 = 48

Solving for variable 'x'.

Reorder the terms:
-48 + 21x + x2 = 48 + -48

Combine like terms: 48 + -48 = 0
-48 + 21x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '48' to each side of the equation.
-48 + 21x + 48 + x2 = 0 + 48

Reorder the terms:
-48 + 48 + 21x + x2 = 0 + 48

Combine like terms: -48 + 48 = 0
0 + 21x + x2 = 0 + 48
21x + x2 = 0 + 48

Combine like terms: 0 + 48 = 48
21x + x2 = 48

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 = 48 + 110.25

Reorder the terms:
110.25 + 21x + x2 = 48 + 110.25

Combine like terms: 48 + 110.25 = 158.25
110.25 + 21x + x2 = 158.25

Factor a perfect square on the left side:
(x + 10.5)(x + 10.5) = 158.25

Calculate the square root of the right side: 12.579745625

Break this problem into two subproblems by setting 
(x + 10.5) equal to 12.579745625 and -12.579745625.

Subproblem 1

x + 10.5 = 12.579745625 Simplifying x + 10.5 = 12.579745625 Reorder the terms: 10.5 + x = 12.579745625 Solving 10.5 + x = 12.579745625 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 = 12.579745625 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = 12.579745625 + -10.5 x = 12.579745625 + -10.5 Combine like terms: 12.579745625 + -10.5 = 2.079745625 x = 2.079745625 Simplifying x = 2.079745625

Subproblem 2

x + 10.5 = -12.579745625 Simplifying x + 10.5 = -12.579745625 Reorder the terms: 10.5 + x = -12.579745625 Solving 10.5 + x = -12.579745625 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 = -12.579745625 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = -12.579745625 + -10.5 x = -12.579745625 + -10.5 Combine like terms: -12.579745625 + -10.5 = -23.079745625 x = -23.079745625 Simplifying x = -23.079745625

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.079745625, -23.079745625}

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