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Simplifying 1 + -9h2 = 12h Solving 1 + -9h2 = 12h Solving for variable 'h'. Reorder the terms: 1 + -12h + -9h2 = 12h + -12h Combine like terms: 12h + -12h = 0 1 + -12h + -9h2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -0.1111111111 + 1.333333333h + h2 = 0 Move the constant term to the right: Add '0.1111111111' to each side of the equation. -0.1111111111 + 1.333333333h + 0.1111111111 + h2 = 0 + 0.1111111111 Reorder the terms: -0.1111111111 + 0.1111111111 + 1.333333333h + h2 = 0 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + 1.333333333h + h2 = 0 + 0.1111111111 1.333333333h + h2 = 0 + 0.1111111111 Combine like terms: 0 + 0.1111111111 = 0.1111111111 1.333333333h + h2 = 0.1111111111 The h term is 1.333333333h. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333h + 0.4444444442 + h2 = 0.1111111111 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333h + h2 = 0.1111111111 + 0.4444444442 Combine like terms: 0.1111111111 + 0.4444444442 = 0.5555555553 0.4444444442 + 1.333333333h + h2 = 0.5555555553 Factor a perfect square on the left side: (h + 0.6666666665)(h + 0.6666666665) = 0.5555555553 Calculate the square root of the right side: 0.745355992 Break this problem into two subproblems by setting (h + 0.6666666665) equal to 0.745355992 and -0.745355992.Subproblem 1
h + 0.6666666665 = 0.745355992 Simplifying h + 0.6666666665 = 0.745355992 Reorder the terms: 0.6666666665 + h = 0.745355992 Solving 0.6666666665 + h = 0.745355992 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + h = 0.745355992 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + h = 0.745355992 + -0.6666666665 h = 0.745355992 + -0.6666666665 Combine like terms: 0.745355992 + -0.6666666665 = 0.0786893255 h = 0.0786893255 Simplifying h = 0.0786893255Subproblem 2
h + 0.6666666665 = -0.745355992 Simplifying h + 0.6666666665 = -0.745355992 Reorder the terms: 0.6666666665 + h = -0.745355992 Solving 0.6666666665 + h = -0.745355992 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + h = -0.745355992 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + h = -0.745355992 + -0.6666666665 h = -0.745355992 + -0.6666666665 Combine like terms: -0.745355992 + -0.6666666665 = -1.4120226585 h = -1.4120226585 Simplifying h = -1.4120226585Solution
The solution to the problem is based on the solutions from the subproblems. h = {0.0786893255, -1.4120226585}
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