x^2+20x-51=0

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Solution for x^2+20x-51=0 equation:


Simplifying
x2 + 20x + -51 = 0

Reorder the terms:
-51 + 20x + x2 = 0

Solving
-51 + 20x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '51' to each side of the equation.
-51 + 20x + 51 + x2 = 0 + 51

Reorder the terms:
-51 + 51 + 20x + x2 = 0 + 51

Combine like terms: -51 + 51 = 0
0 + 20x + x2 = 0 + 51
20x + x2 = 0 + 51

Combine like terms: 0 + 51 = 51
20x + x2 = 51

The x term is 20x.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20x + 100 + x2 = 51 + 100

Reorder the terms:
100 + 20x + x2 = 51 + 100

Combine like terms: 51 + 100 = 151
100 + 20x + x2 = 151

Factor a perfect square on the left side:
(x + 10)(x + 10) = 151

Calculate the square root of the right side: 12.288205727

Break this problem into two subproblems by setting 
(x + 10) equal to 12.288205727 and -12.288205727.

Subproblem 1

x + 10 = 12.288205727 Simplifying x + 10 = 12.288205727 Reorder the terms: 10 + x = 12.288205727 Solving 10 + x = 12.288205727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 12.288205727 + -10 Combine like terms: 10 + -10 = 0 0 + x = 12.288205727 + -10 x = 12.288205727 + -10 Combine like terms: 12.288205727 + -10 = 2.288205727 x = 2.288205727 Simplifying x = 2.288205727

Subproblem 2

x + 10 = -12.288205727 Simplifying x + 10 = -12.288205727 Reorder the terms: 10 + x = -12.288205727 Solving 10 + x = -12.288205727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -12.288205727 + -10 Combine like terms: 10 + -10 = 0 0 + x = -12.288205727 + -10 x = -12.288205727 + -10 Combine like terms: -12.288205727 + -10 = -22.288205727 x = -22.288205727 Simplifying x = -22.288205727

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.288205727, -22.288205727}

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