0=x^2-21x+48

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Solution for 0=x^2-21x+48 equation:


Simplifying
0 = x2 + -21x + 48

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

Solving
0 = 48 + -21x + x2

Solving for variable 'x'.

Combine like terms: 0 + -48 = -48
-48 + 21x + -1x2 = 48 + -21x + x2 + -48 + 21x + -1x2

Reorder the terms:
-48 + 21x + -1x2 = 48 + -48 + -21x + 21x + x2 + -1x2

Combine like terms: 48 + -48 = 0
-48 + 21x + -1x2 = 0 + -21x + 21x + x2 + -1x2
-48 + 21x + -1x2 = -21x + 21x + x2 + -1x2

Combine like terms: -21x + 21x = 0
-48 + 21x + -1x2 = 0 + x2 + -1x2
-48 + 21x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-48 + 21x + -1x2 = 0

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

Divide each side by '-1'.
48 + -21x + x2 = 0

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 = 62.25
110.25 + -21x + x2 = 62.25

Factor a perfect square on the left side:
(x + -10.5)(x + -10.5) = 62.25

Calculate the square root of the right side: 7.889866919

Break this problem into two subproblems by setting 
(x + -10.5) equal to 7.889866919 and -7.889866919.

Subproblem 1

x + -10.5 = 7.889866919 Simplifying x + -10.5 = 7.889866919 Reorder the terms: -10.5 + x = 7.889866919 Solving -10.5 + x = 7.889866919 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 = 7.889866919 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = 7.889866919 + 10.5 x = 7.889866919 + 10.5 Combine like terms: 7.889866919 + 10.5 = 18.389866919 x = 18.389866919 Simplifying x = 18.389866919

Subproblem 2

x + -10.5 = -7.889866919 Simplifying x + -10.5 = -7.889866919 Reorder the terms: -10.5 + x = -7.889866919 Solving -10.5 + x = -7.889866919 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 = -7.889866919 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = -7.889866919 + 10.5 x = -7.889866919 + 10.5 Combine like terms: -7.889866919 + 10.5 = 2.610133081 x = 2.610133081 Simplifying x = 2.610133081

Solution

The solution to the problem is based on the solutions from the subproblems. x = {18.389866919, 2.610133081}

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