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Simplifying h2 + -14h + -11 = 0 Reorder the terms: -11 + -14h + h2 = 0 Solving -11 + -14h + h2 = 0 Solving for variable 'h'. Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + -14h + 11 + h2 = 0 + 11 Reorder the terms: -11 + 11 + -14h + h2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -14h + h2 = 0 + 11 -14h + h2 = 0 + 11 Combine like terms: 0 + 11 = 11 -14h + h2 = 11 The h term is -14h. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14h + 49 + h2 = 11 + 49 Reorder the terms: 49 + -14h + h2 = 11 + 49 Combine like terms: 11 + 49 = 60 49 + -14h + h2 = 60 Factor a perfect square on the left side: (h + -7)(h + -7) = 60 Calculate the square root of the right side: 7.745966692 Break this problem into two subproblems by setting (h + -7) equal to 7.745966692 and -7.745966692.Subproblem 1
h + -7 = 7.745966692 Simplifying h + -7 = 7.745966692 Reorder the terms: -7 + h = 7.745966692 Solving -7 + h = 7.745966692 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + h = 7.745966692 + 7 Combine like terms: -7 + 7 = 0 0 + h = 7.745966692 + 7 h = 7.745966692 + 7 Combine like terms: 7.745966692 + 7 = 14.745966692 h = 14.745966692 Simplifying h = 14.745966692Subproblem 2
h + -7 = -7.745966692 Simplifying h + -7 = -7.745966692 Reorder the terms: -7 + h = -7.745966692 Solving -7 + h = -7.745966692 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + h = -7.745966692 + 7 Combine like terms: -7 + 7 = 0 0 + h = -7.745966692 + 7 h = -7.745966692 + 7 Combine like terms: -7.745966692 + 7 = -0.745966692 h = -0.745966692 Simplifying h = -0.745966692Solution
The solution to the problem is based on the solutions from the subproblems. h = {14.745966692, -0.745966692}
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