51=x^2+21x

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Solution for 51=x^2+21x equation:


Simplifying
51 = x2 + 21x

Reorder the terms:
51 = 21x + x2

Solving
51 = 21x + x2

Solving for variable 'x'.

Reorder the terms:
51 + -21x + -1x2 = 21x + -21x + x2 + -1x2

Combine like terms: 21x + -21x = 0
51 + -21x + -1x2 = 0 + x2 + -1x2
51 + -21x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
51 + -21x + -1x2 = 0

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

Divide each side by '-1'.
-51 + 21x + x2 = 0

Move the constant term to the right:

Add '51' to each side of the equation.
-51 + 21x + 51 + x2 = 0 + 51

Reorder the terms:
-51 + 51 + 21x + x2 = 0 + 51

Combine like terms: -51 + 51 = 0
0 + 21x + x2 = 0 + 51
21x + x2 = 0 + 51

Combine like terms: 0 + 51 = 51
21x + x2 = 51

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 = 51 + 110.25

Reorder the terms:
110.25 + 21x + x2 = 51 + 110.25

Combine like terms: 51 + 110.25 = 161.25
110.25 + 21x + x2 = 161.25

Factor a perfect square on the left side:
(x + 10.5)(x + 10.5) = 161.25

Calculate the square root of the right side: 12.698425099

Break this problem into two subproblems by setting 
(x + 10.5) equal to 12.698425099 and -12.698425099.

Subproblem 1

x + 10.5 = 12.698425099 Simplifying x + 10.5 = 12.698425099 Reorder the terms: 10.5 + x = 12.698425099 Solving 10.5 + x = 12.698425099 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 = 12.698425099 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = 12.698425099 + -10.5 x = 12.698425099 + -10.5 Combine like terms: 12.698425099 + -10.5 = 2.198425099 x = 2.198425099 Simplifying x = 2.198425099

Subproblem 2

x + 10.5 = -12.698425099 Simplifying x + 10.5 = -12.698425099 Reorder the terms: 10.5 + x = -12.698425099 Solving 10.5 + x = -12.698425099 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 = -12.698425099 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = -12.698425099 + -10.5 x = -12.698425099 + -10.5 Combine like terms: -12.698425099 + -10.5 = -23.198425099 x = -23.198425099 Simplifying x = -23.198425099

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.198425099, -23.198425099}

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