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Simplifying 4h2 + 76h = 164 Reorder the terms: 76h + 4h2 = 164 Solving 76h + 4h2 = 164 Solving for variable 'h'. Reorder the terms: -164 + 76h + 4h2 = 164 + -164 Combine like terms: 164 + -164 = 0 -164 + 76h + 4h2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-41 + 19h + h2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-41 + 19h + h2)' equal to zero and attempt to solve: Simplifying -41 + 19h + h2 = 0 Solving -41 + 19h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '41' to each side of the equation. -41 + 19h + 41 + h2 = 0 + 41 Reorder the terms: -41 + 41 + 19h + h2 = 0 + 41 Combine like terms: -41 + 41 = 0 0 + 19h + h2 = 0 + 41 19h + h2 = 0 + 41 Combine like terms: 0 + 41 = 41 19h + h2 = 41 The h term is 19h. Take half its coefficient (9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. 19h + 90.25 + h2 = 41 + 90.25 Reorder the terms: 90.25 + 19h + h2 = 41 + 90.25 Combine like terms: 41 + 90.25 = 131.25 90.25 + 19h + h2 = 131.25 Factor a perfect square on the left side: (h + 9.5)(h + 9.5) = 131.25 Calculate the square root of the right side: 11.456439237 Break this problem into two subproblems by setting (h + 9.5) equal to 11.456439237 and -11.456439237.Subproblem 1
h + 9.5 = 11.456439237 Simplifying h + 9.5 = 11.456439237 Reorder the terms: 9.5 + h = 11.456439237 Solving 9.5 + h = 11.456439237 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + h = 11.456439237 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + h = 11.456439237 + -9.5 h = 11.456439237 + -9.5 Combine like terms: 11.456439237 + -9.5 = 1.956439237 h = 1.956439237 Simplifying h = 1.956439237Subproblem 2
h + 9.5 = -11.456439237 Simplifying h + 9.5 = -11.456439237 Reorder the terms: 9.5 + h = -11.456439237 Solving 9.5 + h = -11.456439237 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + h = -11.456439237 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + h = -11.456439237 + -9.5 h = -11.456439237 + -9.5 Combine like terms: -11.456439237 + -9.5 = -20.956439237 h = -20.956439237 Simplifying h = -20.956439237Solution
The solution to the problem is based on the solutions from the subproblems. h = {1.956439237, -20.956439237}Solution
h = {1.956439237, -20.956439237}
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