h^2+9h-21=0

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Solution for h^2+9h-21=0 equation:


Simplifying
h2 + 9h + -21 = 0

Reorder the terms:
-21 + 9h + h2 = 0

Solving
-21 + 9h + h2 = 0

Solving for variable 'h'.

Begin completing the square.

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + 9h + 21 + h2 = 0 + 21

Reorder the terms:
-21 + 21 + 9h + h2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + 9h + h2 = 0 + 21
9h + h2 = 0 + 21

Combine like terms: 0 + 21 = 21
9h + h2 = 21

The h term is 9h.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9h + 20.25 + h2 = 21 + 20.25

Reorder the terms:
20.25 + 9h + h2 = 21 + 20.25

Combine like terms: 21 + 20.25 = 41.25
20.25 + 9h + h2 = 41.25

Factor a perfect square on the left side:
(h + 4.5)(h + 4.5) = 41.25

Calculate the square root of the right side: 6.422616289

Break this problem into two subproblems by setting 
(h + 4.5) equal to 6.422616289 and -6.422616289.

Subproblem 1

h + 4.5 = 6.422616289 Simplifying h + 4.5 = 6.422616289 Reorder the terms: 4.5 + h = 6.422616289 Solving 4.5 + h = 6.422616289 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + h = 6.422616289 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + h = 6.422616289 + -4.5 h = 6.422616289 + -4.5 Combine like terms: 6.422616289 + -4.5 = 1.922616289 h = 1.922616289 Simplifying h = 1.922616289

Subproblem 2

h + 4.5 = -6.422616289 Simplifying h + 4.5 = -6.422616289 Reorder the terms: 4.5 + h = -6.422616289 Solving 4.5 + h = -6.422616289 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + h = -6.422616289 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + h = -6.422616289 + -4.5 h = -6.422616289 + -4.5 Combine like terms: -6.422616289 + -4.5 = -10.922616289 h = -10.922616289 Simplifying h = -10.922616289

Solution

The solution to the problem is based on the solutions from the subproblems. h = {1.922616289, -10.922616289}

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