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Simplifying (2h2 + -7h + 10) + -1(h2 + 4h + 7) = 0 Reorder the terms: (10 + -7h + 2h2) + -1(h2 + 4h + 7) = 0 Remove parenthesis around (10 + -7h + 2h2) 10 + -7h + 2h2 + -1(h2 + 4h + 7) = 0 Reorder the terms: 10 + -7h + 2h2 + -1(7 + 4h + h2) = 0 10 + -7h + 2h2 + (7 * -1 + 4h * -1 + h2 * -1) = 0 10 + -7h + 2h2 + (-7 + -4h + -1h2) = 0 Reorder the terms: 10 + -7 + -7h + -4h + 2h2 + -1h2 = 0 Combine like terms: 10 + -7 = 3 3 + -7h + -4h + 2h2 + -1h2 = 0 Combine like terms: -7h + -4h = -11h 3 + -11h + 2h2 + -1h2 = 0 Combine like terms: 2h2 + -1h2 = 1h2 3 + -11h + 1h2 = 0 Solving 3 + -11h + 1h2 = 0 Solving for variable 'h'. Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -11h + -3 + h2 = 0 + -3 Reorder the terms: 3 + -3 + -11h + h2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -11h + h2 = 0 + -3 -11h + h2 = 0 + -3 Combine like terms: 0 + -3 = -3 -11h + h2 = -3 The h term is -11h. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11h + 30.25 + h2 = -3 + 30.25 Reorder the terms: 30.25 + -11h + h2 = -3 + 30.25 Combine like terms: -3 + 30.25 = 27.25 30.25 + -11h + h2 = 27.25 Factor a perfect square on the left side: (h + -5.5)(h + -5.5) = 27.25 Calculate the square root of the right side: 5.220153254 Break this problem into two subproblems by setting (h + -5.5) equal to 5.220153254 and -5.220153254.Subproblem 1
h + -5.5 = 5.220153254 Simplifying h + -5.5 = 5.220153254 Reorder the terms: -5.5 + h = 5.220153254 Solving -5.5 + h = 5.220153254 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + h = 5.220153254 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + h = 5.220153254 + 5.5 h = 5.220153254 + 5.5 Combine like terms: 5.220153254 + 5.5 = 10.720153254 h = 10.720153254 Simplifying h = 10.720153254Subproblem 2
h + -5.5 = -5.220153254 Simplifying h + -5.5 = -5.220153254 Reorder the terms: -5.5 + h = -5.220153254 Solving -5.5 + h = -5.220153254 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + h = -5.220153254 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + h = -5.220153254 + 5.5 h = -5.220153254 + 5.5 Combine like terms: -5.220153254 + 5.5 = 0.279846746 h = 0.279846746 Simplifying h = 0.279846746Solution
The solution to the problem is based on the solutions from the subproblems. h = {10.720153254, 0.279846746}
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