h^2+6h-28=0

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Solution for h^2+6h-28=0 equation:


Simplifying
h2 + 6h + -28 = 0

Reorder the terms:
-28 + 6h + h2 = 0

Solving
-28 + 6h + h2 = 0

Solving for variable 'h'.

Begin completing the square.

Move the constant term to the right:

Add '28' to each side of the equation.
-28 + 6h + 28 + h2 = 0 + 28

Reorder the terms:
-28 + 28 + 6h + h2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + 6h + h2 = 0 + 28
6h + h2 = 0 + 28

Combine like terms: 0 + 28 = 28
6h + h2 = 28

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 = 28 + 9

Reorder the terms:
9 + 6h + h2 = 28 + 9

Combine like terms: 28 + 9 = 37
9 + 6h + h2 = 37

Factor a perfect square on the left side:
(h + 3)(h + 3) = 37

Calculate the square root of the right side: 6.08276253

Break this problem into two subproblems by setting 
(h + 3) equal to 6.08276253 and -6.08276253.

Subproblem 1

h + 3 = 6.08276253 Simplifying h + 3 = 6.08276253 Reorder the terms: 3 + h = 6.08276253 Solving 3 + h = 6.08276253 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 = 6.08276253 + -3 Combine like terms: 3 + -3 = 0 0 + h = 6.08276253 + -3 h = 6.08276253 + -3 Combine like terms: 6.08276253 + -3 = 3.08276253 h = 3.08276253 Simplifying h = 3.08276253

Subproblem 2

h + 3 = -6.08276253 Simplifying h + 3 = -6.08276253 Reorder the terms: 3 + h = -6.08276253 Solving 3 + h = -6.08276253 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 = -6.08276253 + -3 Combine like terms: 3 + -3 = 0 0 + h = -6.08276253 + -3 h = -6.08276253 + -3 Combine like terms: -6.08276253 + -3 = -9.08276253 h = -9.08276253 Simplifying h = -9.08276253

Solution

The solution to the problem is based on the solutions from the subproblems. h = {3.08276253, -9.08276253}

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