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Simplifying 5h(11 + -1h) = -5 (11 * 5h + -1h * 5h) = -5 (55h + -5h2) = -5 Solving 55h + -5h2 = -5 Solving for variable 'h'. Reorder the terms: 5 + 55h + -5h2 = -5 + 5 Combine like terms: -5 + 5 = 0 5 + 55h + -5h2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(1 + 11h + -1h2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(1 + 11h + -1h2)' equal to zero and attempt to solve: Simplifying 1 + 11h + -1h2 = 0 Solving 1 + 11h + -1h2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1 + -11h + h2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -11h + 1 + h2 = 0 + 1 Reorder the terms: -1 + 1 + -11h + h2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -11h + h2 = 0 + 1 -11h + h2 = 0 + 1 Combine like terms: 0 + 1 = 1 -11h + h2 = 1 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 = 1 + 30.25 Reorder the terms: 30.25 + -11h + h2 = 1 + 30.25 Combine like terms: 1 + 30.25 = 31.25 30.25 + -11h + h2 = 31.25 Factor a perfect square on the left side: (h + -5.5)(h + -5.5) = 31.25 Calculate the square root of the right side: 5.590169944 Break this problem into two subproblems by setting (h + -5.5) equal to 5.590169944 and -5.590169944.Subproblem 1
h + -5.5 = 5.590169944 Simplifying h + -5.5 = 5.590169944 Reorder the terms: -5.5 + h = 5.590169944 Solving -5.5 + h = 5.590169944 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 = 5.590169944 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + h = 5.590169944 + 5.5 h = 5.590169944 + 5.5 Combine like terms: 5.590169944 + 5.5 = 11.090169944 h = 11.090169944 Simplifying h = 11.090169944Subproblem 2
h + -5.5 = -5.590169944 Simplifying h + -5.5 = -5.590169944 Reorder the terms: -5.5 + h = -5.590169944 Solving -5.5 + h = -5.590169944 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 = -5.590169944 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + h = -5.590169944 + 5.5 h = -5.590169944 + 5.5 Combine like terms: -5.590169944 + 5.5 = -0.090169944 h = -0.090169944 Simplifying h = -0.090169944Solution
The solution to the problem is based on the solutions from the subproblems. h = {11.090169944, -0.090169944}Solution
h = {11.090169944, -0.090169944}
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