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Simplifying h2 + 14h = -25 Reorder the terms: 14h + h2 = -25 Solving 14h + h2 = -25 Solving for variable 'h'. Reorder the terms: 25 + 14h + h2 = -25 + 25 Combine like terms: -25 + 25 = 0 25 + 14h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '-25' to each side of the equation. 25 + 14h + -25 + h2 = 0 + -25 Reorder the terms: 25 + -25 + 14h + h2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + 14h + h2 = 0 + -25 14h + h2 = 0 + -25 Combine like terms: 0 + -25 = -25 14h + h2 = -25 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 = -25 + 49 Reorder the terms: 49 + 14h + h2 = -25 + 49 Combine like terms: -25 + 49 = 24 49 + 14h + h2 = 24 Factor a perfect square on the left side: (h + 7)(h + 7) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (h + 7) equal to 4.898979486 and -4.898979486.Subproblem 1
h + 7 = 4.898979486 Simplifying h + 7 = 4.898979486 Reorder the terms: 7 + h = 4.898979486 Solving 7 + h = 4.898979486 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 = 4.898979486 + -7 Combine like terms: 7 + -7 = 0 0 + h = 4.898979486 + -7 h = 4.898979486 + -7 Combine like terms: 4.898979486 + -7 = -2.101020514 h = -2.101020514 Simplifying h = -2.101020514Subproblem 2
h + 7 = -4.898979486 Simplifying h + 7 = -4.898979486 Reorder the terms: 7 + h = -4.898979486 Solving 7 + h = -4.898979486 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 = -4.898979486 + -7 Combine like terms: 7 + -7 = 0 0 + h = -4.898979486 + -7 h = -4.898979486 + -7 Combine like terms: -4.898979486 + -7 = -11.898979486 h = -11.898979486 Simplifying h = -11.898979486Solution
The solution to the problem is based on the solutions from the subproblems. h = {-2.101020514, -11.898979486}
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