h^2+6h-11=0

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Solution for h^2+6h-11=0 equation:


Simplifying
h2 + 6h + -11 = 0

Reorder the terms:
-11 + 6h + h2 = 0

Solving
-11 + 6h + h2 = 0

Solving for variable 'h'.

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + 6h + 11 + h2 = 0 + 11

Reorder the terms:
-11 + 11 + 6h + h2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + 6h + h2 = 0 + 11
6h + h2 = 0 + 11

Combine like terms: 0 + 11 = 11
6h + h2 = 11

The h term is 6h.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6h + 9 + h2 = 11 + 9

Reorder the terms:
9 + 6h + h2 = 11 + 9

Combine like terms: 11 + 9 = 20
9 + 6h + h2 = 20

Factor a perfect square on the left side:
(h + 3)(h + 3) = 20

Calculate the square root of the right side: 4.472135955

Break this problem into two subproblems by setting 
(h + 3) equal to 4.472135955 and -4.472135955.

Subproblem 1

h + 3 = 4.472135955 Simplifying h + 3 = 4.472135955 Reorder the terms: 3 + h = 4.472135955 Solving 3 + h = 4.472135955 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + h = 4.472135955 + -3 Combine like terms: 3 + -3 = 0 0 + h = 4.472135955 + -3 h = 4.472135955 + -3 Combine like terms: 4.472135955 + -3 = 1.472135955 h = 1.472135955 Simplifying h = 1.472135955

Subproblem 2

h + 3 = -4.472135955 Simplifying h + 3 = -4.472135955 Reorder the terms: 3 + h = -4.472135955 Solving 3 + h = -4.472135955 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + h = -4.472135955 + -3 Combine like terms: 3 + -3 = 0 0 + h = -4.472135955 + -3 h = -4.472135955 + -3 Combine like terms: -4.472135955 + -3 = -7.472135955 h = -7.472135955 Simplifying h = -7.472135955

Solution

The solution to the problem is based on the solutions from the subproblems. h = {1.472135955, -7.472135955}

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