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Simplifying h2 + 7h + -240 = 0 Reorder the terms: -240 + 7h + h2 = 0 Solving -240 + 7h + h2 = 0 Solving for variable 'h'. Begin completing the square. Move the constant term to the right: Add '240' to each side of the equation. -240 + 7h + 240 + h2 = 0 + 240 Reorder the terms: -240 + 240 + 7h + h2 = 0 + 240 Combine like terms: -240 + 240 = 0 0 + 7h + h2 = 0 + 240 7h + h2 = 0 + 240 Combine like terms: 0 + 240 = 240 7h + h2 = 240 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 = 240 + 12.25 Reorder the terms: 12.25 + 7h + h2 = 240 + 12.25 Combine like terms: 240 + 12.25 = 252.25 12.25 + 7h + h2 = 252.25 Factor a perfect square on the left side: (h + 3.5)(h + 3.5) = 252.25 Calculate the square root of the right side: 15.882380174 Break this problem into two subproblems by setting (h + 3.5) equal to 15.882380174 and -15.882380174.Subproblem 1
h + 3.5 = 15.882380174 Simplifying h + 3.5 = 15.882380174 Reorder the terms: 3.5 + h = 15.882380174 Solving 3.5 + h = 15.882380174 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 = 15.882380174 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + h = 15.882380174 + -3.5 h = 15.882380174 + -3.5 Combine like terms: 15.882380174 + -3.5 = 12.382380174 h = 12.382380174 Simplifying h = 12.382380174Subproblem 2
h + 3.5 = -15.882380174 Simplifying h + 3.5 = -15.882380174 Reorder the terms: 3.5 + h = -15.882380174 Solving 3.5 + h = -15.882380174 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 = -15.882380174 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + h = -15.882380174 + -3.5 h = -15.882380174 + -3.5 Combine like terms: -15.882380174 + -3.5 = -19.382380174 h = -19.382380174 Simplifying h = -19.382380174Solution
The solution to the problem is based on the solutions from the subproblems. h = {12.382380174, -19.382380174}
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