-x^2-11x+14=0

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Solution for -x^2-11x+14=0 equation:


Simplifying
-1x2 + -11x + 14 = 0

Reorder the terms:
14 + -11x + -1x2 = 0

Solving
14 + -11x + -1x2 = 0

Solving for variable 'x'.

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

Divide each side by '-1'.
-14 + 11x + x2 = 0

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + 11x + 14 + x2 = 0 + 14

Reorder the terms:
-14 + 14 + 11x + x2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + 11x + x2 = 0 + 14
11x + x2 = 0 + 14

Combine like terms: 0 + 14 = 14
11x + x2 = 14

The x term is 11x.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11x + 30.25 + x2 = 14 + 30.25

Reorder the terms:
30.25 + 11x + x2 = 14 + 30.25

Combine like terms: 14 + 30.25 = 44.25
30.25 + 11x + x2 = 44.25

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 44.25

Calculate the square root of the right side: 6.652067348

Break this problem into two subproblems by setting 
(x + 5.5) equal to 6.652067348 and -6.652067348.

Subproblem 1

x + 5.5 = 6.652067348 Simplifying x + 5.5 = 6.652067348 Reorder the terms: 5.5 + x = 6.652067348 Solving 5.5 + x = 6.652067348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 6.652067348 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 6.652067348 + -5.5 x = 6.652067348 + -5.5 Combine like terms: 6.652067348 + -5.5 = 1.152067348 x = 1.152067348 Simplifying x = 1.152067348

Subproblem 2

x + 5.5 = -6.652067348 Simplifying x + 5.5 = -6.652067348 Reorder the terms: 5.5 + x = -6.652067348 Solving 5.5 + x = -6.652067348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -6.652067348 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -6.652067348 + -5.5 x = -6.652067348 + -5.5 Combine like terms: -6.652067348 + -5.5 = -12.152067348 x = -12.152067348 Simplifying x = -12.152067348

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.152067348, -12.152067348}

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