a^2-21a+48=0

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


Simplifying
a2 + -21a + 48 = 0

Reorder the terms:
48 + -21a + a2 = 0

Solving
48 + -21a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '-48' to each side of the equation.
48 + -21a + -48 + a2 = 0 + -48

Reorder the terms:
48 + -48 + -21a + a2 = 0 + -48

Combine like terms: 48 + -48 = 0
0 + -21a + a2 = 0 + -48
-21a + a2 = 0 + -48

Combine like terms: 0 + -48 = -48
-21a + a2 = -48

The a term is -21a.  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.
-21a + 110.25 + a2 = -48 + 110.25

Reorder the terms:
110.25 + -21a + a2 = -48 + 110.25

Combine like terms: -48 + 110.25 = 62.25
110.25 + -21a + a2 = 62.25

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

Calculate the square root of the right side: 7.889866919

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

Subproblem 1

a + -10.5 = 7.889866919 Simplifying a + -10.5 = 7.889866919 Reorder the terms: -10.5 + a = 7.889866919 Solving -10.5 + a = 7.889866919 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + a = 7.889866919 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + a = 7.889866919 + 10.5 a = 7.889866919 + 10.5 Combine like terms: 7.889866919 + 10.5 = 18.389866919 a = 18.389866919 Simplifying a = 18.389866919

Subproblem 2

a + -10.5 = -7.889866919 Simplifying a + -10.5 = -7.889866919 Reorder the terms: -10.5 + a = -7.889866919 Solving -10.5 + a = -7.889866919 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + a = -7.889866919 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + a = -7.889866919 + 10.5 a = -7.889866919 + 10.5 Combine like terms: -7.889866919 + 10.5 = 2.610133081 a = 2.610133081 Simplifying a = 2.610133081

Solution

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

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