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Simplifying 0 = h2 + 12h + -135 Reorder the terms: 0 = -135 + 12h + h2 Solving 0 = -135 + 12h + h2 Solving for variable 'h'. Combine like terms: 0 + 135 = 135 135 + -12h + -1h2 = -135 + 12h + h2 + 135 + -12h + -1h2 Reorder the terms: 135 + -12h + -1h2 = -135 + 135 + 12h + -12h + h2 + -1h2 Combine like terms: -135 + 135 = 0 135 + -12h + -1h2 = 0 + 12h + -12h + h2 + -1h2 135 + -12h + -1h2 = 12h + -12h + h2 + -1h2 Combine like terms: 12h + -12h = 0 135 + -12h + -1h2 = 0 + h2 + -1h2 135 + -12h + -1h2 = h2 + -1h2 Combine like terms: h2 + -1h2 = 0 135 + -12h + -1h2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -135 + 12h + h2 = 0 Move the constant term to the right: Add '135' to each side of the equation. -135 + 12h + 135 + h2 = 0 + 135 Reorder the terms: -135 + 135 + 12h + h2 = 0 + 135 Combine like terms: -135 + 135 = 0 0 + 12h + h2 = 0 + 135 12h + h2 = 0 + 135 Combine like terms: 0 + 135 = 135 12h + h2 = 135 The h term is 12h. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12h + 36 + h2 = 135 + 36 Reorder the terms: 36 + 12h + h2 = 135 + 36 Combine like terms: 135 + 36 = 171 36 + 12h + h2 = 171 Factor a perfect square on the left side: (h + 6)(h + 6) = 171 Calculate the square root of the right side: 13.076696831 Break this problem into two subproblems by setting (h + 6) equal to 13.076696831 and -13.076696831.Subproblem 1
h + 6 = 13.076696831 Simplifying h + 6 = 13.076696831 Reorder the terms: 6 + h = 13.076696831 Solving 6 + h = 13.076696831 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + h = 13.076696831 + -6 Combine like terms: 6 + -6 = 0 0 + h = 13.076696831 + -6 h = 13.076696831 + -6 Combine like terms: 13.076696831 + -6 = 7.076696831 h = 7.076696831 Simplifying h = 7.076696831Subproblem 2
h + 6 = -13.076696831 Simplifying h + 6 = -13.076696831 Reorder the terms: 6 + h = -13.076696831 Solving 6 + h = -13.076696831 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + h = -13.076696831 + -6 Combine like terms: 6 + -6 = 0 0 + h = -13.076696831 + -6 h = -13.076696831 + -6 Combine like terms: -13.076696831 + -6 = -19.076696831 h = -19.076696831 Simplifying h = -19.076696831Solution
The solution to the problem is based on the solutions from the subproblems. h = {7.076696831, -19.076696831}
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