h^2+3h-22=0

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Solution for h^2+3h-22=0 equation:


Simplifying
h2 + 3h + -22 = 0

Reorder the terms:
-22 + 3h + h2 = 0

Solving
-22 + 3h + h2 = 0

Solving for variable 'h'.

Begin completing the square.

Move the constant term to the right:

Add '22' to each side of the equation.
-22 + 3h + 22 + h2 = 0 + 22

Reorder the terms:
-22 + 22 + 3h + h2 = 0 + 22

Combine like terms: -22 + 22 = 0
0 + 3h + h2 = 0 + 22
3h + h2 = 0 + 22

Combine like terms: 0 + 22 = 22
3h + h2 = 22

The h term is 3h.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3h + 2.25 + h2 = 22 + 2.25

Reorder the terms:
2.25 + 3h + h2 = 22 + 2.25

Combine like terms: 22 + 2.25 = 24.25
2.25 + 3h + h2 = 24.25

Factor a perfect square on the left side:
(h + 1.5)(h + 1.5) = 24.25

Calculate the square root of the right side: 4.924428901

Break this problem into two subproblems by setting 
(h + 1.5) equal to 4.924428901 and -4.924428901.

Subproblem 1

h + 1.5 = 4.924428901 Simplifying h + 1.5 = 4.924428901 Reorder the terms: 1.5 + h = 4.924428901 Solving 1.5 + h = 4.924428901 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + h = 4.924428901 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + h = 4.924428901 + -1.5 h = 4.924428901 + -1.5 Combine like terms: 4.924428901 + -1.5 = 3.424428901 h = 3.424428901 Simplifying h = 3.424428901

Subproblem 2

h + 1.5 = -4.924428901 Simplifying h + 1.5 = -4.924428901 Reorder the terms: 1.5 + h = -4.924428901 Solving 1.5 + h = -4.924428901 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + h = -4.924428901 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + h = -4.924428901 + -1.5 h = -4.924428901 + -1.5 Combine like terms: -4.924428901 + -1.5 = -6.424428901 h = -6.424428901 Simplifying h = -6.424428901

Solution

The solution to the problem is based on the solutions from the subproblems. h = {3.424428901, -6.424428901}

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