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Simplifying -2h2 + 28h + 98 = 0 Reorder the terms: 98 + 28h + -2h2 = 0 Solving 98 + 28h + -2h2 = 0 Solving for variable 'h'. Factor out the Greatest Common Factor (GCF), '2'. 2(49 + 14h + -1h2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(49 + 14h + -1h2)' equal to zero and attempt to solve: Simplifying 49 + 14h + -1h2 = 0 Solving 49 + 14h + -1h2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -49 + -14h + h2 = 0 Move the constant term to the right: Add '49' to each side of the equation. -49 + -14h + 49 + h2 = 0 + 49 Reorder the terms: -49 + 49 + -14h + h2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + -14h + h2 = 0 + 49 -14h + h2 = 0 + 49 Combine like terms: 0 + 49 = 49 -14h + h2 = 49 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 = 49 + 49 Reorder the terms: 49 + -14h + h2 = 49 + 49 Combine like terms: 49 + 49 = 98 49 + -14h + h2 = 98 Factor a perfect square on the left side: (h + -7)(h + -7) = 98 Calculate the square root of the right side: 9.899494937 Break this problem into two subproblems by setting (h + -7) equal to 9.899494937 and -9.899494937.Subproblem 1
h + -7 = 9.899494937 Simplifying h + -7 = 9.899494937 Reorder the terms: -7 + h = 9.899494937 Solving -7 + h = 9.899494937 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 = 9.899494937 + 7 Combine like terms: -7 + 7 = 0 0 + h = 9.899494937 + 7 h = 9.899494937 + 7 Combine like terms: 9.899494937 + 7 = 16.899494937 h = 16.899494937 Simplifying h = 16.899494937Subproblem 2
h + -7 = -9.899494937 Simplifying h + -7 = -9.899494937 Reorder the terms: -7 + h = -9.899494937 Solving -7 + h = -9.899494937 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 = -9.899494937 + 7 Combine like terms: -7 + 7 = 0 0 + h = -9.899494937 + 7 h = -9.899494937 + 7 Combine like terms: -9.899494937 + 7 = -2.899494937 h = -2.899494937 Simplifying h = -2.899494937Solution
The solution to the problem is based on the solutions from the subproblems. h = {16.899494937, -2.899494937}Solution
h = {16.899494937, -2.899494937}
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