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Simplifying 0.5h + 0.333h(h + -6) = 0.833h + 2 Reorder the terms: 0.5h + 0.333h(-6 + h) = 0.833h + 2 0.5h + (-6 * 0.333h + h * 0.333h) = 0.833h + 2 0.5h + (-1.998h + 0.333h2) = 0.833h + 2 Combine like terms: 0.5h + -1.998h = -1.498h -1.498h + 0.333h2 = 0.833h + 2 Reorder the terms: -1.498h + 0.333h2 = 2 + 0.833h Solving -1.498h + 0.333h2 = 2 + 0.833h Solving for variable 'h'. Reorder the terms: -2 + -1.498h + -0.833h + 0.333h2 = 2 + 0.833h + -2 + -0.833h Combine like terms: -1.498h + -0.833h = -2.331h -2 + -2.331h + 0.333h2 = 2 + 0.833h + -2 + -0.833h Reorder the terms: -2 + -2.331h + 0.333h2 = 2 + -2 + 0.833h + -0.833h Combine like terms: 2 + -2 = 0 -2 + -2.331h + 0.333h2 = 0 + 0.833h + -0.833h -2 + -2.331h + 0.333h2 = 0.833h + -0.833h Combine like terms: 0.833h + -0.833h = 0.000 -2 + -2.331h + 0.333h2 = 0.000 Begin completing the square. Divide all terms by 0.333 the coefficient of the squared term: Divide each side by '0.333'. -6.006006006 + -7h + h2 = 0 Move the constant term to the right: Add '6.006006006' to each side of the equation. -6.006006006 + -7h + 6.006006006 + h2 = 0 + 6.006006006 Reorder the terms: -6.006006006 + 6.006006006 + -7h + h2 = 0 + 6.006006006 Combine like terms: -6.006006006 + 6.006006006 = 0.000000000 0.000000000 + -7h + h2 = 0 + 6.006006006 -7h + h2 = 0 + 6.006006006 Combine like terms: 0 + 6.006006006 = 6.006006006 -7h + h2 = 6.006006006 The h term is -7h. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7h + 12.25 + h2 = 6.006006006 + 12.25 Reorder the terms: 12.25 + -7h + h2 = 6.006006006 + 12.25 Combine like terms: 6.006006006 + 12.25 = 18.256006006 12.25 + -7h + h2 = 18.256006006 Factor a perfect square on the left side: (h + -3.5)(h + -3.5) = 18.256006006 Calculate the square root of the right side: 4.272704765 Break this problem into two subproblems by setting (h + -3.5) equal to 4.272704765 and -4.272704765.Subproblem 1
h + -3.5 = 4.272704765 Simplifying h + -3.5 = 4.272704765 Reorder the terms: -3.5 + h = 4.272704765 Solving -3.5 + h = 4.272704765 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + h = 4.272704765 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + h = 4.272704765 + 3.5 h = 4.272704765 + 3.5 Combine like terms: 4.272704765 + 3.5 = 7.772704765 h = 7.772704765 Simplifying h = 7.772704765Subproblem 2
h + -3.5 = -4.272704765 Simplifying h + -3.5 = -4.272704765 Reorder the terms: -3.5 + h = -4.272704765 Solving -3.5 + h = -4.272704765 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + h = -4.272704765 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + h = -4.272704765 + 3.5 h = -4.272704765 + 3.5 Combine like terms: -4.272704765 + 3.5 = -0.772704765 h = -0.772704765 Simplifying h = -0.772704765Solution
The solution to the problem is based on the solutions from the subproblems. h = {7.772704765, -0.772704765}
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