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Simplifying 12 + -7h = h2 Solving 12 + -7h = h2 Solving for variable 'h'. Combine like terms: h2 + -1h2 = 0 12 + -7h + -1h2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -12 + 7h + h2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + 7h + 12 + h2 = 0 + 12 Reorder the terms: -12 + 12 + 7h + h2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 7h + h2 = 0 + 12 7h + h2 = 0 + 12 Combine like terms: 0 + 12 = 12 7h + h2 = 12 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 = 12 + 12.25 Reorder the terms: 12.25 + 7h + h2 = 12 + 12.25 Combine like terms: 12 + 12.25 = 24.25 12.25 + 7h + h2 = 24.25 Factor a perfect square on the left side: (h + 3.5)(h + 3.5) = 24.25 Calculate the square root of the right side: 4.924428901 Break this problem into two subproblems by setting (h + 3.5) equal to 4.924428901 and -4.924428901.Subproblem 1
h + 3.5 = 4.924428901 Simplifying h + 3.5 = 4.924428901 Reorder the terms: 3.5 + h = 4.924428901 Solving 3.5 + h = 4.924428901 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 = 4.924428901 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + h = 4.924428901 + -3.5 h = 4.924428901 + -3.5 Combine like terms: 4.924428901 + -3.5 = 1.424428901 h = 1.424428901 Simplifying h = 1.424428901Subproblem 2
h + 3.5 = -4.924428901 Simplifying h + 3.5 = -4.924428901 Reorder the terms: 3.5 + h = -4.924428901 Solving 3.5 + h = -4.924428901 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 = -4.924428901 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + h = -4.924428901 + -3.5 h = -4.924428901 + -3.5 Combine like terms: -4.924428901 + -3.5 = -8.424428901 h = -8.424428901 Simplifying h = -8.424428901Solution
The solution to the problem is based on the solutions from the subproblems. h = {1.424428901, -8.424428901}
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