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Simplifying -4h(-1h3 + -8h2 + 2h) = 0 Reorder the terms: -4h(2h + -8h2 + -1h3) = 0 (2h * -4h + -8h2 * -4h + -1h3 * -4h) = 0 (-8h2 + 32h3 + 4h4) = 0 Solving -8h2 + 32h3 + 4h4 = 0 Solving for variable 'h'. Factor out the Greatest Common Factor (GCF), '4h2'. 4h2(-2 + 8h + h2) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'h2' equal to zero and attempt to solve: Simplifying h2 = 0 Solving h2 = 0 Move all terms containing h to the left, all other terms to the right. Simplifying h2 = 0 Take the square root of each side: h = {0}Subproblem 2
Set the factor '(-2 + 8h + h2)' equal to zero and attempt to solve: Simplifying -2 + 8h + h2 = 0 Solving -2 + 8h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 8h + 2 + h2 = 0 + 2 Reorder the terms: -2 + 2 + 8h + h2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 8h + h2 = 0 + 2 8h + h2 = 0 + 2 Combine like terms: 0 + 2 = 2 8h + h2 = 2 The h term is 8h. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8h + 16 + h2 = 2 + 16 Reorder the terms: 16 + 8h + h2 = 2 + 16 Combine like terms: 2 + 16 = 18 16 + 8h + h2 = 18 Factor a perfect square on the left side: (h + 4)(h + 4) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (h + 4) equal to 4.242640687 and -4.242640687.Subproblem 1
h + 4 = 4.242640687 Simplifying h + 4 = 4.242640687 Reorder the terms: 4 + h = 4.242640687 Solving 4 + h = 4.242640687 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + h = 4.242640687 + -4 Combine like terms: 4 + -4 = 0 0 + h = 4.242640687 + -4 h = 4.242640687 + -4 Combine like terms: 4.242640687 + -4 = 0.242640687 h = 0.242640687 Simplifying h = 0.242640687Subproblem 2
h + 4 = -4.242640687 Simplifying h + 4 = -4.242640687 Reorder the terms: 4 + h = -4.242640687 Solving 4 + h = -4.242640687 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + h = -4.242640687 + -4 Combine like terms: 4 + -4 = 0 0 + h = -4.242640687 + -4 h = -4.242640687 + -4 Combine like terms: -4.242640687 + -4 = -8.242640687 h = -8.242640687 Simplifying h = -8.242640687Solution
The solution to the problem is based on the solutions from the subproblems. h = {0.242640687, -8.242640687}Solution
h = {0, 0.242640687, -8.242640687}
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