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Simplifying 4h2 + 56h = -124 Reorder the terms: 56h + 4h2 = -124 Solving 56h + 4h2 = -124 Solving for variable 'h'. Reorder the terms: 124 + 56h + 4h2 = -124 + 124 Combine like terms: -124 + 124 = 0 124 + 56h + 4h2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(31 + 14h + h2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(31 + 14h + h2)' equal to zero and attempt to solve: Simplifying 31 + 14h + h2 = 0 Solving 31 + 14h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '-31' to each side of the equation. 31 + 14h + -31 + h2 = 0 + -31 Reorder the terms: 31 + -31 + 14h + h2 = 0 + -31 Combine like terms: 31 + -31 = 0 0 + 14h + h2 = 0 + -31 14h + h2 = 0 + -31 Combine like terms: 0 + -31 = -31 14h + h2 = -31 The h term is 14h. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14h + 49 + h2 = -31 + 49 Reorder the terms: 49 + 14h + h2 = -31 + 49 Combine like terms: -31 + 49 = 18 49 + 14h + h2 = 18 Factor a perfect square on the left side: (h + 7)(h + 7) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (h + 7) equal to 4.242640687 and -4.242640687.Subproblem 1
h + 7 = 4.242640687 Simplifying h + 7 = 4.242640687 Reorder the terms: 7 + h = 4.242640687 Solving 7 + h = 4.242640687 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + h = 4.242640687 + -7 Combine like terms: 7 + -7 = 0 0 + h = 4.242640687 + -7 h = 4.242640687 + -7 Combine like terms: 4.242640687 + -7 = -2.757359313 h = -2.757359313 Simplifying h = -2.757359313Subproblem 2
h + 7 = -4.242640687 Simplifying h + 7 = -4.242640687 Reorder the terms: 7 + h = -4.242640687 Solving 7 + h = -4.242640687 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + h = -4.242640687 + -7 Combine like terms: 7 + -7 = 0 0 + h = -4.242640687 + -7 h = -4.242640687 + -7 Combine like terms: -4.242640687 + -7 = -11.242640687 h = -11.242640687 Simplifying h = -11.242640687Solution
The solution to the problem is based on the solutions from the subproblems. h = {-2.757359313, -11.242640687}Solution
h = {-2.757359313, -11.242640687}
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