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Simplifying -3h2 + -30h = 21 Reorder the terms: -30h + -3h2 = 21 Solving -30h + -3h2 = 21 Solving for variable 'h'. Reorder the terms: -21 + -30h + -3h2 = 21 + -21 Combine like terms: 21 + -21 = 0 -21 + -30h + -3h2 = 0 Factor out the Greatest Common Factor (GCF), '-3'. -3(7 + 10h + h2) = 0 Ignore the factor -3.Subproblem 1
Set the factor '(7 + 10h + h2)' equal to zero and attempt to solve: Simplifying 7 + 10h + h2 = 0 Solving 7 + 10h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + 10h + -7 + h2 = 0 + -7 Reorder the terms: 7 + -7 + 10h + h2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 10h + h2 = 0 + -7 10h + h2 = 0 + -7 Combine like terms: 0 + -7 = -7 10h + h2 = -7 The h term is 10h. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10h + 25 + h2 = -7 + 25 Reorder the terms: 25 + 10h + h2 = -7 + 25 Combine like terms: -7 + 25 = 18 25 + 10h + h2 = 18 Factor a perfect square on the left side: (h + 5)(h + 5) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (h + 5) equal to 4.242640687 and -4.242640687.Subproblem 1
h + 5 = 4.242640687 Simplifying h + 5 = 4.242640687 Reorder the terms: 5 + h = 4.242640687 Solving 5 + h = 4.242640687 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + h = 4.242640687 + -5 Combine like terms: 5 + -5 = 0 0 + h = 4.242640687 + -5 h = 4.242640687 + -5 Combine like terms: 4.242640687 + -5 = -0.757359313 h = -0.757359313 Simplifying h = -0.757359313Subproblem 2
h + 5 = -4.242640687 Simplifying h + 5 = -4.242640687 Reorder the terms: 5 + h = -4.242640687 Solving 5 + h = -4.242640687 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + h = -4.242640687 + -5 Combine like terms: 5 + -5 = 0 0 + h = -4.242640687 + -5 h = -4.242640687 + -5 Combine like terms: -4.242640687 + -5 = -9.242640687 h = -9.242640687 Simplifying h = -9.242640687Solution
The solution to the problem is based on the solutions from the subproblems. h = {-0.757359313, -9.242640687}Solution
h = {-0.757359313, -9.242640687}
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