x^2+20x-43=0

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Solution for x^2+20x-43=0 equation:


Simplifying
x2 + 20x + -43 = 0

Reorder the terms:
-43 + 20x + x2 = 0

Solving
-43 + 20x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '43' to each side of the equation.
-43 + 20x + 43 + x2 = 0 + 43

Reorder the terms:
-43 + 43 + 20x + x2 = 0 + 43

Combine like terms: -43 + 43 = 0
0 + 20x + x2 = 0 + 43
20x + x2 = 0 + 43

Combine like terms: 0 + 43 = 43
20x + x2 = 43

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 = 43 + 100

Reorder the terms:
100 + 20x + x2 = 43 + 100

Combine like terms: 43 + 100 = 143
100 + 20x + x2 = 143

Factor a perfect square on the left side:
(x + 10)(x + 10) = 143

Calculate the square root of the right side: 11.958260743

Break this problem into two subproblems by setting 
(x + 10) equal to 11.958260743 and -11.958260743.

Subproblem 1

x + 10 = 11.958260743 Simplifying x + 10 = 11.958260743 Reorder the terms: 10 + x = 11.958260743 Solving 10 + x = 11.958260743 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 = 11.958260743 + -10 Combine like terms: 10 + -10 = 0 0 + x = 11.958260743 + -10 x = 11.958260743 + -10 Combine like terms: 11.958260743 + -10 = 1.958260743 x = 1.958260743 Simplifying x = 1.958260743

Subproblem 2

x + 10 = -11.958260743 Simplifying x + 10 = -11.958260743 Reorder the terms: 10 + x = -11.958260743 Solving 10 + x = -11.958260743 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 = -11.958260743 + -10 Combine like terms: 10 + -10 = 0 0 + x = -11.958260743 + -10 x = -11.958260743 + -10 Combine like terms: -11.958260743 + -10 = -21.958260743 x = -21.958260743 Simplifying x = -21.958260743

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.958260743, -21.958260743}

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