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Simplifying (8h + -1) + -1(h + 3) * h = -3 Reorder the terms: (-1 + 8h) + -1(h + 3) * h = -3 Remove parenthesis around (-1 + 8h) -1 + 8h + -1(h + 3) * h = -3 Reorder the terms: -1 + 8h + -1(3 + h) * h = -3 Reorder the terms for easier multiplication: -1 + 8h + -1h(3 + h) = -3 -1 + 8h + (3 * -1h + h * -1h) = -3 -1 + 8h + (-3h + -1h2) = -3 Combine like terms: 8h + -3h = 5h -1 + 5h + -1h2 = -3 Solving -1 + 5h + -1h2 = -3 Solving for variable 'h'. Reorder the terms: -1 + 3 + 5h + -1h2 = -3 + 3 Combine like terms: -1 + 3 = 2 2 + 5h + -1h2 = -3 + 3 Combine like terms: -3 + 3 = 0 2 + 5h + -1h2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2 + -5h + h2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -5h + 2 + h2 = 0 + 2 Reorder the terms: -2 + 2 + -5h + h2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -5h + h2 = 0 + 2 -5h + h2 = 0 + 2 Combine like terms: 0 + 2 = 2 -5h + h2 = 2 The h term is -5h. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5h + 6.25 + h2 = 2 + 6.25 Reorder the terms: 6.25 + -5h + h2 = 2 + 6.25 Combine like terms: 2 + 6.25 = 8.25 6.25 + -5h + h2 = 8.25 Factor a perfect square on the left side: (h + -2.5)(h + -2.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (h + -2.5) equal to 2.872281323 and -2.872281323.Subproblem 1
h + -2.5 = 2.872281323 Simplifying h + -2.5 = 2.872281323 Reorder the terms: -2.5 + h = 2.872281323 Solving -2.5 + h = 2.872281323 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + h = 2.872281323 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + h = 2.872281323 + 2.5 h = 2.872281323 + 2.5 Combine like terms: 2.872281323 + 2.5 = 5.372281323 h = 5.372281323 Simplifying h = 5.372281323Subproblem 2
h + -2.5 = -2.872281323 Simplifying h + -2.5 = -2.872281323 Reorder the terms: -2.5 + h = -2.872281323 Solving -2.5 + h = -2.872281323 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + h = -2.872281323 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + h = -2.872281323 + 2.5 h = -2.872281323 + 2.5 Combine like terms: -2.872281323 + 2.5 = -0.372281323 h = -0.372281323 Simplifying h = -0.372281323Solution
The solution to the problem is based on the solutions from the subproblems. h = {5.372281323, -0.372281323}
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