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Simplifying -4h2 + 64h + 36 = 0 Reorder the terms: 36 + 64h + -4h2 = 0 Solving 36 + 64h + -4h2 = 0 Solving for variable 'h'. Factor out the Greatest Common Factor (GCF), '4'. 4(9 + 16h + -1h2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(9 + 16h + -1h2)' equal to zero and attempt to solve: Simplifying 9 + 16h + -1h2 = 0 Solving 9 + 16h + -1h2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -9 + -16h + h2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -16h + 9 + h2 = 0 + 9 Reorder the terms: -9 + 9 + -16h + h2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -16h + h2 = 0 + 9 -16h + h2 = 0 + 9 Combine like terms: 0 + 9 = 9 -16h + h2 = 9 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 = 9 + 64 Reorder the terms: 64 + -16h + h2 = 9 + 64 Combine like terms: 9 + 64 = 73 64 + -16h + h2 = 73 Factor a perfect square on the left side: (h + -8)(h + -8) = 73 Calculate the square root of the right side: 8.544003745 Break this problem into two subproblems by setting (h + -8) equal to 8.544003745 and -8.544003745.Subproblem 1
h + -8 = 8.544003745 Simplifying h + -8 = 8.544003745 Reorder the terms: -8 + h = 8.544003745 Solving -8 + h = 8.544003745 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 = 8.544003745 + 8 Combine like terms: -8 + 8 = 0 0 + h = 8.544003745 + 8 h = 8.544003745 + 8 Combine like terms: 8.544003745 + 8 = 16.544003745 h = 16.544003745 Simplifying h = 16.544003745Subproblem 2
h + -8 = -8.544003745 Simplifying h + -8 = -8.544003745 Reorder the terms: -8 + h = -8.544003745 Solving -8 + h = -8.544003745 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 = -8.544003745 + 8 Combine like terms: -8 + 8 = 0 0 + h = -8.544003745 + 8 h = -8.544003745 + 8 Combine like terms: -8.544003745 + 8 = -0.544003745 h = -0.544003745 Simplifying h = -0.544003745Solution
The solution to the problem is based on the solutions from the subproblems. h = {16.544003745, -0.544003745}Solution
h = {16.544003745, -0.544003745}
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