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Simplifying (86 + -1h)(h) = 86 Reorder the terms for easier multiplication: h(86 + -1h) = 86 (86 * h + -1h * h) = 86 (86h + -1h2) = 86 Solving 86h + -1h2 = 86 Solving for variable 'h'. Reorder the terms: -86 + 86h + -1h2 = 86 + -86 Combine like terms: 86 + -86 = 0 -86 + 86h + -1h2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 86 + -86h + h2 = 0 Move the constant term to the right: Add '-86' to each side of the equation. 86 + -86h + -86 + h2 = 0 + -86 Reorder the terms: 86 + -86 + -86h + h2 = 0 + -86 Combine like terms: 86 + -86 = 0 0 + -86h + h2 = 0 + -86 -86h + h2 = 0 + -86 Combine like terms: 0 + -86 = -86 -86h + h2 = -86 The h term is -86h. Take half its coefficient (-43). Square it (1849) and add it to both sides. Add '1849' to each side of the equation. -86h + 1849 + h2 = -86 + 1849 Reorder the terms: 1849 + -86h + h2 = -86 + 1849 Combine like terms: -86 + 1849 = 1763 1849 + -86h + h2 = 1763 Factor a perfect square on the left side: (h + -43)(h + -43) = 1763 Calculate the square root of the right side: 41.98809355 Break this problem into two subproblems by setting (h + -43) equal to 41.98809355 and -41.98809355.Subproblem 1
h + -43 = 41.98809355 Simplifying h + -43 = 41.98809355 Reorder the terms: -43 + h = 41.98809355 Solving -43 + h = 41.98809355 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '43' to each side of the equation. -43 + 43 + h = 41.98809355 + 43 Combine like terms: -43 + 43 = 0 0 + h = 41.98809355 + 43 h = 41.98809355 + 43 Combine like terms: 41.98809355 + 43 = 84.98809355 h = 84.98809355 Simplifying h = 84.98809355Subproblem 2
h + -43 = -41.98809355 Simplifying h + -43 = -41.98809355 Reorder the terms: -43 + h = -41.98809355 Solving -43 + h = -41.98809355 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '43' to each side of the equation. -43 + 43 + h = -41.98809355 + 43 Combine like terms: -43 + 43 = 0 0 + h = -41.98809355 + 43 h = -41.98809355 + 43 Combine like terms: -41.98809355 + 43 = 1.01190645 h = 1.01190645 Simplifying h = 1.01190645Solution
The solution to the problem is based on the solutions from the subproblems. h = {84.98809355, 1.01190645}
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