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Simplifying 0 = 5h2 + 12h + -4896 Reorder the terms: 0 = -4896 + 12h + 5h2 Solving 0 = -4896 + 12h + 5h2 Solving for variable 'h'. Combine like terms: 0 + 4896 = 4896 4896 + -12h + -5h2 = -4896 + 12h + 5h2 + 4896 + -12h + -5h2 Reorder the terms: 4896 + -12h + -5h2 = -4896 + 4896 + 12h + -12h + 5h2 + -5h2 Combine like terms: -4896 + 4896 = 0 4896 + -12h + -5h2 = 0 + 12h + -12h + 5h2 + -5h2 4896 + -12h + -5h2 = 12h + -12h + 5h2 + -5h2 Combine like terms: 12h + -12h = 0 4896 + -12h + -5h2 = 0 + 5h2 + -5h2 4896 + -12h + -5h2 = 5h2 + -5h2 Combine like terms: 5h2 + -5h2 = 0 4896 + -12h + -5h2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -979.2 + 2.4h + h2 = 0 Move the constant term to the right: Add '979.2' to each side of the equation. -979.2 + 2.4h + 979.2 + h2 = 0 + 979.2 Reorder the terms: -979.2 + 979.2 + 2.4h + h2 = 0 + 979.2 Combine like terms: -979.2 + 979.2 = 0.0 0.0 + 2.4h + h2 = 0 + 979.2 2.4h + h2 = 0 + 979.2 Combine like terms: 0 + 979.2 = 979.2 2.4h + h2 = 979.2 The h term is 2.4h. Take half its coefficient (1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. 2.4h + 1.44 + h2 = 979.2 + 1.44 Reorder the terms: 1.44 + 2.4h + h2 = 979.2 + 1.44 Combine like terms: 979.2 + 1.44 = 980.64 1.44 + 2.4h + h2 = 980.64 Factor a perfect square on the left side: (h + 1.2)(h + 1.2) = 980.64 Calculate the square root of the right side: 31.315172042 Break this problem into two subproblems by setting (h + 1.2) equal to 31.315172042 and -31.315172042.Subproblem 1
h + 1.2 = 31.315172042 Simplifying h + 1.2 = 31.315172042 Reorder the terms: 1.2 + h = 31.315172042 Solving 1.2 + h = 31.315172042 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + h = 31.315172042 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + h = 31.315172042 + -1.2 h = 31.315172042 + -1.2 Combine like terms: 31.315172042 + -1.2 = 30.115172042 h = 30.115172042 Simplifying h = 30.115172042Subproblem 2
h + 1.2 = -31.315172042 Simplifying h + 1.2 = -31.315172042 Reorder the terms: 1.2 + h = -31.315172042 Solving 1.2 + h = -31.315172042 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + h = -31.315172042 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + h = -31.315172042 + -1.2 h = -31.315172042 + -1.2 Combine like terms: -31.315172042 + -1.2 = -32.515172042 h = -32.515172042 Simplifying h = -32.515172042Solution
The solution to the problem is based on the solutions from the subproblems. h = {30.115172042, -32.515172042}
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