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Simplifying 5h2 + -5h + -155 = 0 Reorder the terms: -155 + -5h + 5h2 = 0 Solving -155 + -5h + 5h2 = 0 Solving for variable 'h'. Factor out the Greatest Common Factor (GCF), '5'. 5(-31 + -1h + h2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-31 + -1h + h2)' equal to zero and attempt to solve: Simplifying -31 + -1h + h2 = 0 Solving -31 + -1h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '31' to each side of the equation. -31 + -1h + 31 + h2 = 0 + 31 Reorder the terms: -31 + 31 + -1h + h2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + -1h + h2 = 0 + 31 -1h + h2 = 0 + 31 Combine like terms: 0 + 31 = 31 -1h + h2 = 31 The h term is -1h. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1h + 0.25 + h2 = 31 + 0.25 Reorder the terms: 0.25 + -1h + h2 = 31 + 0.25 Combine like terms: 31 + 0.25 = 31.25 0.25 + -1h + h2 = 31.25 Factor a perfect square on the left side: (h + -0.5)(h + -0.5) = 31.25 Calculate the square root of the right side: 5.590169944 Break this problem into two subproblems by setting (h + -0.5) equal to 5.590169944 and -5.590169944.Subproblem 1
h + -0.5 = 5.590169944 Simplifying h + -0.5 = 5.590169944 Reorder the terms: -0.5 + h = 5.590169944 Solving -0.5 + h = 5.590169944 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + h = 5.590169944 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + h = 5.590169944 + 0.5 h = 5.590169944 + 0.5 Combine like terms: 5.590169944 + 0.5 = 6.090169944 h = 6.090169944 Simplifying h = 6.090169944Subproblem 2
h + -0.5 = -5.590169944 Simplifying h + -0.5 = -5.590169944 Reorder the terms: -0.5 + h = -5.590169944 Solving -0.5 + h = -5.590169944 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + h = -5.590169944 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + h = -5.590169944 + 0.5 h = -5.590169944 + 0.5 Combine like terms: -5.590169944 + 0.5 = -5.090169944 h = -5.090169944 Simplifying h = -5.090169944Solution
The solution to the problem is based on the solutions from the subproblems. h = {6.090169944, -5.090169944}Solution
h = {6.090169944, -5.090169944}
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