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Simplifying -4h2 + -56h = 156 Reorder the terms: -56h + -4h2 = 156 Solving -56h + -4h2 = 156 Solving for variable 'h'. Reorder the terms: -156 + -56h + -4h2 = 156 + -156 Combine like terms: 156 + -156 = 0 -156 + -56h + -4h2 = 0 Factor out the Greatest Common Factor (GCF), '-4'. -4(39 + 14h + h2) = 0 Ignore the factor -4.Subproblem 1
Set the factor '(39 + 14h + h2)' equal to zero and attempt to solve: Simplifying 39 + 14h + h2 = 0 Solving 39 + 14h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '-39' to each side of the equation. 39 + 14h + -39 + h2 = 0 + -39 Reorder the terms: 39 + -39 + 14h + h2 = 0 + -39 Combine like terms: 39 + -39 = 0 0 + 14h + h2 = 0 + -39 14h + h2 = 0 + -39 Combine like terms: 0 + -39 = -39 14h + h2 = -39 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 = -39 + 49 Reorder the terms: 49 + 14h + h2 = -39 + 49 Combine like terms: -39 + 49 = 10 49 + 14h + h2 = 10 Factor a perfect square on the left side: (h + 7)(h + 7) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (h + 7) equal to 3.16227766 and -3.16227766.Subproblem 1
h + 7 = 3.16227766 Simplifying h + 7 = 3.16227766 Reorder the terms: 7 + h = 3.16227766 Solving 7 + h = 3.16227766 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 = 3.16227766 + -7 Combine like terms: 7 + -7 = 0 0 + h = 3.16227766 + -7 h = 3.16227766 + -7 Combine like terms: 3.16227766 + -7 = -3.83772234 h = -3.83772234 Simplifying h = -3.83772234Subproblem 2
h + 7 = -3.16227766 Simplifying h + 7 = -3.16227766 Reorder the terms: 7 + h = -3.16227766 Solving 7 + h = -3.16227766 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 = -3.16227766 + -7 Combine like terms: 7 + -7 = 0 0 + h = -3.16227766 + -7 h = -3.16227766 + -7 Combine like terms: -3.16227766 + -7 = -10.16227766 h = -10.16227766 Simplifying h = -10.16227766Solution
The solution to the problem is based on the solutions from the subproblems. h = {-3.83772234, -10.16227766}Solution
h = {-3.83772234, -10.16227766}
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