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Simplifying h2 + -4h + -6 = 0 Reorder the terms: -6 + -4h + h2 = 0 Solving -6 + -4h + h2 = 0 Solving for variable 'h'. Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -4h + 6 + h2 = 0 + 6 Reorder the terms: -6 + 6 + -4h + h2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -4h + h2 = 0 + 6 -4h + h2 = 0 + 6 Combine like terms: 0 + 6 = 6 -4h + h2 = 6 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 = 6 + 4 Reorder the terms: 4 + -4h + h2 = 6 + 4 Combine like terms: 6 + 4 = 10 4 + -4h + h2 = 10 Factor a perfect square on the left side: (h + -2)(h + -2) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (h + -2) equal to 3.16227766 and -3.16227766.Subproblem 1
h + -2 = 3.16227766 Simplifying h + -2 = 3.16227766 Reorder the terms: -2 + h = 3.16227766 Solving -2 + h = 3.16227766 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 = 3.16227766 + 2 Combine like terms: -2 + 2 = 0 0 + h = 3.16227766 + 2 h = 3.16227766 + 2 Combine like terms: 3.16227766 + 2 = 5.16227766 h = 5.16227766 Simplifying h = 5.16227766Subproblem 2
h + -2 = -3.16227766 Simplifying h + -2 = -3.16227766 Reorder the terms: -2 + h = -3.16227766 Solving -2 + h = -3.16227766 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 = -3.16227766 + 2 Combine like terms: -2 + 2 = 0 0 + h = -3.16227766 + 2 h = -3.16227766 + 2 Combine like terms: -3.16227766 + 2 = -1.16227766 h = -1.16227766 Simplifying h = -1.16227766Solution
The solution to the problem is based on the solutions from the subproblems. h = {5.16227766, -1.16227766}
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