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Simplifying -4h2 + 64h + 116 = 0 Reorder the terms: 116 + 64h + -4h2 = 0 Solving 116 + 64h + -4h2 = 0 Solving for variable 'h'. Factor out the Greatest Common Factor (GCF), '4'. 4(29 + 16h + -1h2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(29 + 16h + -1h2)' equal to zero and attempt to solve: Simplifying 29 + 16h + -1h2 = 0 Solving 29 + 16h + -1h2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -29 + -16h + h2 = 0 Move the constant term to the right: Add '29' to each side of the equation. -29 + -16h + 29 + h2 = 0 + 29 Reorder the terms: -29 + 29 + -16h + h2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + -16h + h2 = 0 + 29 -16h + h2 = 0 + 29 Combine like terms: 0 + 29 = 29 -16h + h2 = 29 The h term is -16h. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16h + 64 + h2 = 29 + 64 Reorder the terms: 64 + -16h + h2 = 29 + 64 Combine like terms: 29 + 64 = 93 64 + -16h + h2 = 93 Factor a perfect square on the left side: (h + -8)(h + -8) = 93 Calculate the square root of the right side: 9.643650761 Break this problem into two subproblems by setting (h + -8) equal to 9.643650761 and -9.643650761.Subproblem 1
h + -8 = 9.643650761 Simplifying h + -8 = 9.643650761 Reorder the terms: -8 + h = 9.643650761 Solving -8 + h = 9.643650761 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + h = 9.643650761 + 8 Combine like terms: -8 + 8 = 0 0 + h = 9.643650761 + 8 h = 9.643650761 + 8 Combine like terms: 9.643650761 + 8 = 17.643650761 h = 17.643650761 Simplifying h = 17.643650761Subproblem 2
h + -8 = -9.643650761 Simplifying h + -8 = -9.643650761 Reorder the terms: -8 + h = -9.643650761 Solving -8 + h = -9.643650761 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + h = -9.643650761 + 8 Combine like terms: -8 + 8 = 0 0 + h = -9.643650761 + 8 h = -9.643650761 + 8 Combine like terms: -9.643650761 + 8 = -1.643650761 h = -1.643650761 Simplifying h = -1.643650761Solution
The solution to the problem is based on the solutions from the subproblems. h = {17.643650761, -1.643650761}Solution
h = {17.643650761, -1.643650761}
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