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Simplifying 15h2 + 20h + -30 = 0 Reorder the terms: -30 + 20h + 15h2 = 0 Solving -30 + 20h + 15h2 = 0 Solving for variable 'h'. Factor out the Greatest Common Factor (GCF), '5'. 5(-6 + 4h + 3h2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-6 + 4h + 3h2)' equal to zero and attempt to solve: Simplifying -6 + 4h + 3h2 = 0 Solving -6 + 4h + 3h2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2 + 1.333333333h + h2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 1.333333333h + 2 + h2 = 0 + 2 Reorder the terms: -2 + 2 + 1.333333333h + h2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 1.333333333h + h2 = 0 + 2 1.333333333h + h2 = 0 + 2 Combine like terms: 0 + 2 = 2 1.333333333h + h2 = 2 The h term is 1.333333333h. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333h + 0.4444444442 + h2 = 2 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333h + h2 = 2 + 0.4444444442 Combine like terms: 2 + 0.4444444442 = 2.4444444442 0.4444444442 + 1.333333333h + h2 = 2.4444444442 Factor a perfect square on the left side: (h + 0.6666666665)(h + 0.6666666665) = 2.4444444442 Calculate the square root of the right side: 1.56347192 Break this problem into two subproblems by setting (h + 0.6666666665) equal to 1.56347192 and -1.56347192.Subproblem 1
h + 0.6666666665 = 1.56347192 Simplifying h + 0.6666666665 = 1.56347192 Reorder the terms: 0.6666666665 + h = 1.56347192 Solving 0.6666666665 + h = 1.56347192 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + h = 1.56347192 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + h = 1.56347192 + -0.6666666665 h = 1.56347192 + -0.6666666665 Combine like terms: 1.56347192 + -0.6666666665 = 0.8968052535 h = 0.8968052535 Simplifying h = 0.8968052535Subproblem 2
h + 0.6666666665 = -1.56347192 Simplifying h + 0.6666666665 = -1.56347192 Reorder the terms: 0.6666666665 + h = -1.56347192 Solving 0.6666666665 + h = -1.56347192 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + h = -1.56347192 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + h = -1.56347192 + -0.6666666665 h = -1.56347192 + -0.6666666665 Combine like terms: -1.56347192 + -0.6666666665 = -2.2301385865 h = -2.2301385865 Simplifying h = -2.2301385865Solution
The solution to the problem is based on the solutions from the subproblems. h = {0.8968052535, -2.2301385865}Solution
h = {0.8968052535, -2.2301385865}
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