x^2+28x+43=

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Solution for x^2+28x+43= equation:


Simplifying
x2 + 28x + 43 = 0

Reorder the terms:
43 + 28x + x2 = 0

Solving
43 + 28x + 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 + 28x + -43 + x2 = 0 + -43

Reorder the terms:
43 + -43 + 28x + x2 = 0 + -43

Combine like terms: 43 + -43 = 0
0 + 28x + x2 = 0 + -43
28x + x2 = 0 + -43

Combine like terms: 0 + -43 = -43
28x + x2 = -43

The x term is 28x.  Take half its coefficient (14).
Square it (196) and add it to both sides.

Add '196' to each side of the equation.
28x + 196 + x2 = -43 + 196

Reorder the terms:
196 + 28x + x2 = -43 + 196

Combine like terms: -43 + 196 = 153
196 + 28x + x2 = 153

Factor a perfect square on the left side:
(x + 14)(x + 14) = 153

Calculate the square root of the right side: 12.369316877

Break this problem into two subproblems by setting 
(x + 14) equal to 12.369316877 and -12.369316877.

Subproblem 1

x + 14 = 12.369316877 Simplifying x + 14 = 12.369316877 Reorder the terms: 14 + x = 12.369316877 Solving 14 + x = 12.369316877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = 12.369316877 + -14 Combine like terms: 14 + -14 = 0 0 + x = 12.369316877 + -14 x = 12.369316877 + -14 Combine like terms: 12.369316877 + -14 = -1.630683123 x = -1.630683123 Simplifying x = -1.630683123

Subproblem 2

x + 14 = -12.369316877 Simplifying x + 14 = -12.369316877 Reorder the terms: 14 + x = -12.369316877 Solving 14 + x = -12.369316877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = -12.369316877 + -14 Combine like terms: 14 + -14 = 0 0 + x = -12.369316877 + -14 x = -12.369316877 + -14 Combine like terms: -12.369316877 + -14 = -26.369316877 x = -26.369316877 Simplifying x = -26.369316877

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.630683123, -26.369316877}

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