5h^2+2h-2=0

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Solution for 5h^2+2h-2=0 equation:


Simplifying
5h2 + 2h + -2 = 0

Reorder the terms:
-2 + 2h + 5h2 = 0

Solving
-2 + 2h + 5h2 = 0

Solving for variable 'h'.

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

Divide each side by '5'.
-0.4 + 0.4h + h2 = 0

Move the constant term to the right:

Add '0.4' to each side of the equation.
-0.4 + 0.4h + 0.4 + h2 = 0 + 0.4

Reorder the terms:
-0.4 + 0.4 + 0.4h + h2 = 0 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + 0.4h + h2 = 0 + 0.4
0.4h + h2 = 0 + 0.4

Combine like terms: 0 + 0.4 = 0.4
0.4h + h2 = 0.4

The h term is 0.4h.  Take half its coefficient (0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
0.4h + 0.04 + h2 = 0.4 + 0.04

Reorder the terms:
0.04 + 0.4h + h2 = 0.4 + 0.04

Combine like terms: 0.4 + 0.04 = 0.44
0.04 + 0.4h + h2 = 0.44

Factor a perfect square on the left side:
(h + 0.2)(h + 0.2) = 0.44

Calculate the square root of the right side: 0.663324958

Break this problem into two subproblems by setting 
(h + 0.2) equal to 0.663324958 and -0.663324958.

Subproblem 1

h + 0.2 = 0.663324958 Simplifying h + 0.2 = 0.663324958 Reorder the terms: 0.2 + h = 0.663324958 Solving 0.2 + h = 0.663324958 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + h = 0.663324958 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + h = 0.663324958 + -0.2 h = 0.663324958 + -0.2 Combine like terms: 0.663324958 + -0.2 = 0.463324958 h = 0.463324958 Simplifying h = 0.463324958

Subproblem 2

h + 0.2 = -0.663324958 Simplifying h + 0.2 = -0.663324958 Reorder the terms: 0.2 + h = -0.663324958 Solving 0.2 + h = -0.663324958 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + h = -0.663324958 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + h = -0.663324958 + -0.2 h = -0.663324958 + -0.2 Combine like terms: -0.663324958 + -0.2 = -0.863324958 h = -0.863324958 Simplifying h = -0.863324958

Solution

The solution to the problem is based on the solutions from the subproblems. h = {0.463324958, -0.863324958}

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