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Simplifying h2 + -4h = 29 Reorder the terms: -4h + h2 = 29 Solving -4h + h2 = 29 Solving for variable 'h'. Reorder the terms: -29 + -4h + h2 = 29 + -29 Combine like terms: 29 + -29 = 0 -29 + -4h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '29' to each side of the equation. -29 + -4h + 29 + h2 = 0 + 29 Reorder the terms: -29 + 29 + -4h + h2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + -4h + h2 = 0 + 29 -4h + h2 = 0 + 29 Combine like terms: 0 + 29 = 29 -4h + h2 = 29 The h term is -4h. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4h + 4 + h2 = 29 + 4 Reorder the terms: 4 + -4h + h2 = 29 + 4 Combine like terms: 29 + 4 = 33 4 + -4h + h2 = 33 Factor a perfect square on the left side: (h + -2)(h + -2) = 33 Calculate the square root of the right side: 5.744562647 Break this problem into two subproblems by setting (h + -2) equal to 5.744562647 and -5.744562647.Subproblem 1
h + -2 = 5.744562647 Simplifying h + -2 = 5.744562647 Reorder the terms: -2 + h = 5.744562647 Solving -2 + h = 5.744562647 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + h = 5.744562647 + 2 Combine like terms: -2 + 2 = 0 0 + h = 5.744562647 + 2 h = 5.744562647 + 2 Combine like terms: 5.744562647 + 2 = 7.744562647 h = 7.744562647 Simplifying h = 7.744562647Subproblem 2
h + -2 = -5.744562647 Simplifying h + -2 = -5.744562647 Reorder the terms: -2 + h = -5.744562647 Solving -2 + h = -5.744562647 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + h = -5.744562647 + 2 Combine like terms: -2 + 2 = 0 0 + h = -5.744562647 + 2 h = -5.744562647 + 2 Combine like terms: -5.744562647 + 2 = -3.744562647 h = -3.744562647 Simplifying h = -3.744562647Solution
The solution to the problem is based on the solutions from the subproblems. h = {7.744562647, -3.744562647}
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