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Simplifying -4h2 + -8h = -28 Reorder the terms: -8h + -4h2 = -28 Solving -8h + -4h2 = -28 Solving for variable 'h'. Reorder the terms: 28 + -8h + -4h2 = -28 + 28 Combine like terms: -28 + 28 = 0 28 + -8h + -4h2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(7 + -2h + -1h2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(7 + -2h + -1h2)' equal to zero and attempt to solve: Simplifying 7 + -2h + -1h2 = 0 Solving 7 + -2h + -1h2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -7 + 2h + h2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + 2h + 7 + h2 = 0 + 7 Reorder the terms: -7 + 7 + 2h + h2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 2h + h2 = 0 + 7 2h + h2 = 0 + 7 Combine like terms: 0 + 7 = 7 2h + h2 = 7 The h term is 2h. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2h + 1 + h2 = 7 + 1 Reorder the terms: 1 + 2h + h2 = 7 + 1 Combine like terms: 7 + 1 = 8 1 + 2h + h2 = 8 Factor a perfect square on the left side: (h + 1)(h + 1) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (h + 1) equal to 2.828427125 and -2.828427125.Subproblem 1
h + 1 = 2.828427125 Simplifying h + 1 = 2.828427125 Reorder the terms: 1 + h = 2.828427125 Solving 1 + h = 2.828427125 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + h = 2.828427125 + -1 Combine like terms: 1 + -1 = 0 0 + h = 2.828427125 + -1 h = 2.828427125 + -1 Combine like terms: 2.828427125 + -1 = 1.828427125 h = 1.828427125 Simplifying h = 1.828427125Subproblem 2
h + 1 = -2.828427125 Simplifying h + 1 = -2.828427125 Reorder the terms: 1 + h = -2.828427125 Solving 1 + h = -2.828427125 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + h = -2.828427125 + -1 Combine like terms: 1 + -1 = 0 0 + h = -2.828427125 + -1 h = -2.828427125 + -1 Combine like terms: -2.828427125 + -1 = -3.828427125 h = -3.828427125 Simplifying h = -3.828427125Solution
The solution to the problem is based on the solutions from the subproblems. h = {1.828427125, -3.828427125}Solution
h = {1.828427125, -3.828427125}
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