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Simplifying h2 + -3h = 258 Reorder the terms: -3h + h2 = 258 Solving -3h + h2 = 258 Solving for variable 'h'. Reorder the terms: -258 + -3h + h2 = 258 + -258 Combine like terms: 258 + -258 = 0 -258 + -3h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '258' to each side of the equation. -258 + -3h + 258 + h2 = 0 + 258 Reorder the terms: -258 + 258 + -3h + h2 = 0 + 258 Combine like terms: -258 + 258 = 0 0 + -3h + h2 = 0 + 258 -3h + h2 = 0 + 258 Combine like terms: 0 + 258 = 258 -3h + h2 = 258 The h term is -3h. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3h + 2.25 + h2 = 258 + 2.25 Reorder the terms: 2.25 + -3h + h2 = 258 + 2.25 Combine like terms: 258 + 2.25 = 260.25 2.25 + -3h + h2 = 260.25 Factor a perfect square on the left side: (h + -1.5)(h + -1.5) = 260.25 Calculate the square root of the right side: 16.132265805 Break this problem into two subproblems by setting (h + -1.5) equal to 16.132265805 and -16.132265805.Subproblem 1
h + -1.5 = 16.132265805 Simplifying h + -1.5 = 16.132265805 Reorder the terms: -1.5 + h = 16.132265805 Solving -1.5 + h = 16.132265805 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + h = 16.132265805 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + h = 16.132265805 + 1.5 h = 16.132265805 + 1.5 Combine like terms: 16.132265805 + 1.5 = 17.632265805 h = 17.632265805 Simplifying h = 17.632265805Subproblem 2
h + -1.5 = -16.132265805 Simplifying h + -1.5 = -16.132265805 Reorder the terms: -1.5 + h = -16.132265805 Solving -1.5 + h = -16.132265805 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + h = -16.132265805 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + h = -16.132265805 + 1.5 h = -16.132265805 + 1.5 Combine like terms: -16.132265805 + 1.5 = -14.632265805 h = -14.632265805 Simplifying h = -14.632265805Solution
The solution to the problem is based on the solutions from the subproblems. h = {17.632265805, -14.632265805}
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