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Simplifying 7(4 + h) * h = 9 Reorder the terms for easier multiplication: 7h(4 + h) = 9 (4 * 7h + h * 7h) = 9 (28h + 7h2) = 9 Solving 28h + 7h2 = 9 Solving for variable 'h'. Reorder the terms: -9 + 28h + 7h2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + 28h + 7h2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.285714286 + 4h + h2 = 0 Move the constant term to the right: Add '1.285714286' to each side of the equation. -1.285714286 + 4h + 1.285714286 + h2 = 0 + 1.285714286 Reorder the terms: -1.285714286 + 1.285714286 + 4h + h2 = 0 + 1.285714286 Combine like terms: -1.285714286 + 1.285714286 = 0.000000000 0.000000000 + 4h + h2 = 0 + 1.285714286 4h + h2 = 0 + 1.285714286 Combine like terms: 0 + 1.285714286 = 1.285714286 4h + h2 = 1.285714286 The h term is 4h. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4h + 4 + h2 = 1.285714286 + 4 Reorder the terms: 4 + 4h + h2 = 1.285714286 + 4 Combine like terms: 1.285714286 + 4 = 5.285714286 4 + 4h + h2 = 5.285714286 Factor a perfect square on the left side: (h + 2)(h + 2) = 5.285714286 Calculate the square root of the right side: 2.299068134 Break this problem into two subproblems by setting (h + 2) equal to 2.299068134 and -2.299068134.Subproblem 1
h + 2 = 2.299068134 Simplifying h + 2 = 2.299068134 Reorder the terms: 2 + h = 2.299068134 Solving 2 + h = 2.299068134 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + h = 2.299068134 + -2 Combine like terms: 2 + -2 = 0 0 + h = 2.299068134 + -2 h = 2.299068134 + -2 Combine like terms: 2.299068134 + -2 = 0.299068134 h = 0.299068134 Simplifying h = 0.299068134Subproblem 2
h + 2 = -2.299068134 Simplifying h + 2 = -2.299068134 Reorder the terms: 2 + h = -2.299068134 Solving 2 + h = -2.299068134 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + h = -2.299068134 + -2 Combine like terms: 2 + -2 = 0 0 + h = -2.299068134 + -2 h = -2.299068134 + -2 Combine like terms: -2.299068134 + -2 = -4.299068134 h = -4.299068134 Simplifying h = -4.299068134Solution
The solution to the problem is based on the solutions from the subproblems. h = {0.299068134, -4.299068134}
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