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Simplifying 9 + 18h + -9h2 = 0 Solving 9 + 18h + -9h2 = 0 Solving for variable 'h'. Factor out the Greatest Common Factor (GCF), '9'. 9(1 + 2h + -1h2) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(1 + 2h + -1h2)' equal to zero and attempt to solve: Simplifying 1 + 2h + -1h2 = 0 Solving 1 + 2h + -1h2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1 + -2h + h2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -2h + 1 + h2 = 0 + 1 Reorder the terms: -1 + 1 + -2h + h2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2h + h2 = 0 + 1 -2h + h2 = 0 + 1 Combine like terms: 0 + 1 = 1 -2h + h2 = 1 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 = 1 + 1 Reorder the terms: 1 + -2h + h2 = 1 + 1 Combine like terms: 1 + 1 = 2 1 + -2h + h2 = 2 Factor a perfect square on the left side: (h + -1)(h + -1) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (h + -1) equal to 1.414213562 and -1.414213562.Subproblem 1
h + -1 = 1.414213562 Simplifying h + -1 = 1.414213562 Reorder the terms: -1 + h = 1.414213562 Solving -1 + h = 1.414213562 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 = 1.414213562 + 1 Combine like terms: -1 + 1 = 0 0 + h = 1.414213562 + 1 h = 1.414213562 + 1 Combine like terms: 1.414213562 + 1 = 2.414213562 h = 2.414213562 Simplifying h = 2.414213562Subproblem 2
h + -1 = -1.414213562 Simplifying h + -1 = -1.414213562 Reorder the terms: -1 + h = -1.414213562 Solving -1 + h = -1.414213562 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 = -1.414213562 + 1 Combine like terms: -1 + 1 = 0 0 + h = -1.414213562 + 1 h = -1.414213562 + 1 Combine like terms: -1.414213562 + 1 = -0.414213562 h = -0.414213562 Simplifying h = -0.414213562Solution
The solution to the problem is based on the solutions from the subproblems. h = {2.414213562, -0.414213562}Solution
h = {2.414213562, -0.414213562}
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