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Simplifying (h3 + -2h) + (3h2 + 4h) + -2h3 = 0 Reorder the terms: (-2h + h3) + (3h2 + 4h) + -2h3 = 0 Remove parenthesis around (-2h + h3) -2h + h3 + (3h2 + 4h) + -2h3 = 0 Reorder the terms: -2h + h3 + (4h + 3h2) + -2h3 = 0 Remove parenthesis around (4h + 3h2) -2h + h3 + 4h + 3h2 + -2h3 = 0 Reorder the terms: -2h + 4h + 3h2 + h3 + -2h3 = 0 Combine like terms: -2h + 4h = 2h 2h + 3h2 + h3 + -2h3 = 0 Combine like terms: h3 + -2h3 = -1h3 2h + 3h2 + -1h3 = 0 Solving 2h + 3h2 + -1h3 = 0 Solving for variable 'h'. Factor out the Greatest Common Factor (GCF), 'h'. h(2 + 3h + -1h2) = 0Subproblem 1
Set the factor 'h' equal to zero and attempt to solve: Simplifying h = 0 Solving h = 0 Move all terms containing h to the left, all other terms to the right. Simplifying h = 0Subproblem 2
Set the factor '(2 + 3h + -1h2)' equal to zero and attempt to solve: Simplifying 2 + 3h + -1h2 = 0 Solving 2 + 3h + -1h2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2 + -3h + h2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -3h + 2 + h2 = 0 + 2 Reorder the terms: -2 + 2 + -3h + h2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3h + h2 = 0 + 2 -3h + h2 = 0 + 2 Combine like terms: 0 + 2 = 2 -3h + h2 = 2 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 = 2 + 2.25 Reorder the terms: 2.25 + -3h + h2 = 2 + 2.25 Combine like terms: 2 + 2.25 = 4.25 2.25 + -3h + h2 = 4.25 Factor a perfect square on the left side: (h + -1.5)(h + -1.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (h + -1.5) equal to 2.061552813 and -2.061552813.Subproblem 1
h + -1.5 = 2.061552813 Simplifying h + -1.5 = 2.061552813 Reorder the terms: -1.5 + h = 2.061552813 Solving -1.5 + h = 2.061552813 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 = 2.061552813 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + h = 2.061552813 + 1.5 h = 2.061552813 + 1.5 Combine like terms: 2.061552813 + 1.5 = 3.561552813 h = 3.561552813 Simplifying h = 3.561552813Subproblem 2
h + -1.5 = -2.061552813 Simplifying h + -1.5 = -2.061552813 Reorder the terms: -1.5 + h = -2.061552813 Solving -1.5 + h = -2.061552813 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 = -2.061552813 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + h = -2.061552813 + 1.5 h = -2.061552813 + 1.5 Combine like terms: -2.061552813 + 1.5 = -0.561552813 h = -0.561552813 Simplifying h = -0.561552813Solution
The solution to the problem is based on the solutions from the subproblems. h = {3.561552813, -0.561552813}Solution
h = {0, 3.561552813, -0.561552813}
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