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Simplifying 12h2 + -84h + 104 = 0 Reorder the terms: 104 + -84h + 12h2 = 0 Solving 104 + -84h + 12h2 = 0 Solving for variable 'h'. Factor out the Greatest Common Factor (GCF), '4'. 4(26 + -21h + 3h2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(26 + -21h + 3h2)' equal to zero and attempt to solve: Simplifying 26 + -21h + 3h2 = 0 Solving 26 + -21h + 3h2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 8.666666667 + -7h + h2 = 0 Move the constant term to the right: Add '-8.666666667' to each side of the equation. 8.666666667 + -7h + -8.666666667 + h2 = 0 + -8.666666667 Reorder the terms: 8.666666667 + -8.666666667 + -7h + h2 = 0 + -8.666666667 Combine like terms: 8.666666667 + -8.666666667 = 0.000000000 0.000000000 + -7h + h2 = 0 + -8.666666667 -7h + h2 = 0 + -8.666666667 Combine like terms: 0 + -8.666666667 = -8.666666667 -7h + h2 = -8.666666667 The h term is -7h. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7h + 12.25 + h2 = -8.666666667 + 12.25 Reorder the terms: 12.25 + -7h + h2 = -8.666666667 + 12.25 Combine like terms: -8.666666667 + 12.25 = 3.583333333 12.25 + -7h + h2 = 3.583333333 Factor a perfect square on the left side: (h + -3.5)(h + -3.5) = 3.583333333 Calculate the square root of the right side: 1.892969449 Break this problem into two subproblems by setting (h + -3.5) equal to 1.892969449 and -1.892969449.Subproblem 1
h + -3.5 = 1.892969449 Simplifying h + -3.5 = 1.892969449 Reorder the terms: -3.5 + h = 1.892969449 Solving -3.5 + h = 1.892969449 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + h = 1.892969449 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + h = 1.892969449 + 3.5 h = 1.892969449 + 3.5 Combine like terms: 1.892969449 + 3.5 = 5.392969449 h = 5.392969449 Simplifying h = 5.392969449Subproblem 2
h + -3.5 = -1.892969449 Simplifying h + -3.5 = -1.892969449 Reorder the terms: -3.5 + h = -1.892969449 Solving -3.5 + h = -1.892969449 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + h = -1.892969449 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + h = -1.892969449 + 3.5 h = -1.892969449 + 3.5 Combine like terms: -1.892969449 + 3.5 = 1.607030551 h = 1.607030551 Simplifying h = 1.607030551Solution
The solution to the problem is based on the solutions from the subproblems. h = {5.392969449, 1.607030551}Solution
h = {5.392969449, 1.607030551}
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