3h^2+6h=15

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Solution for 3h^2+6h=15 equation:


Simplifying
3h2 + 6h = 15

Reorder the terms:
6h + 3h2 = 15

Solving
6h + 3h2 = 15

Solving for variable 'h'.

Reorder the terms:
-15 + 6h + 3h2 = 15 + -15

Combine like terms: 15 + -15 = 0
-15 + 6h + 3h2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + 2h + h2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-5 + 2h + h2)' equal to zero and attempt to solve: Simplifying -5 + 2h + h2 = 0 Solving -5 + 2h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + 2h + 5 + h2 = 0 + 5 Reorder the terms: -5 + 5 + 2h + h2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 2h + h2 = 0 + 5 2h + h2 = 0 + 5 Combine like terms: 0 + 5 = 5 2h + h2 = 5 The h term is 2h. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2h + 1 + h2 = 5 + 1 Reorder the terms: 1 + 2h + h2 = 5 + 1 Combine like terms: 5 + 1 = 6 1 + 2h + h2 = 6 Factor a perfect square on the left side: (h + 1)(h + 1) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (h + 1) equal to 2.449489743 and -2.449489743.

Subproblem 1

h + 1 = 2.449489743 Simplifying h + 1 = 2.449489743 Reorder the terms: 1 + h = 2.449489743 Solving 1 + h = 2.449489743 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + h = 2.449489743 + -1 Combine like terms: 1 + -1 = 0 0 + h = 2.449489743 + -1 h = 2.449489743 + -1 Combine like terms: 2.449489743 + -1 = 1.449489743 h = 1.449489743 Simplifying h = 1.449489743

Subproblem 2

h + 1 = -2.449489743 Simplifying h + 1 = -2.449489743 Reorder the terms: 1 + h = -2.449489743 Solving 1 + h = -2.449489743 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + h = -2.449489743 + -1 Combine like terms: 1 + -1 = 0 0 + h = -2.449489743 + -1 h = -2.449489743 + -1 Combine like terms: -2.449489743 + -1 = -3.449489743 h = -3.449489743 Simplifying h = -3.449489743

Solution

The solution to the problem is based on the solutions from the subproblems. h = {1.449489743, -3.449489743}

Solution

h = {1.449489743, -3.449489743}

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