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Simplifying 91X2 + 72X + -36 = 0 Reorder the terms: -36 + 72X + 91X2 = 0 Solving -36 + 72X + 91X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 91 the coefficient of the squared term: Divide each side by '91'. -0.3956043956 + 0.7912087912X + X2 = 0 Move the constant term to the right: Add '0.3956043956' to each side of the equation. -0.3956043956 + 0.7912087912X + 0.3956043956 + X2 = 0 + 0.3956043956 Reorder the terms: -0.3956043956 + 0.3956043956 + 0.7912087912X + X2 = 0 + 0.3956043956 Combine like terms: -0.3956043956 + 0.3956043956 = 0.0000000000 0.0000000000 + 0.7912087912X + X2 = 0 + 0.3956043956 0.7912087912X + X2 = 0 + 0.3956043956 Combine like terms: 0 + 0.3956043956 = 0.3956043956 0.7912087912X + X2 = 0.3956043956 The X term is 0.7912087912X. Take half its coefficient (0.3956043956). Square it (0.1565028378) and add it to both sides. Add '0.1565028378' to each side of the equation. 0.7912087912X + 0.1565028378 + X2 = 0.3956043956 + 0.1565028378 Reorder the terms: 0.1565028378 + 0.7912087912X + X2 = 0.3956043956 + 0.1565028378 Combine like terms: 0.3956043956 + 0.1565028378 = 0.5521072334 0.1565028378 + 0.7912087912X + X2 = 0.5521072334 Factor a perfect square on the left side: (X + 0.3956043956)(X + 0.3956043956) = 0.5521072334 Calculate the square root of the right side: 0.743039187 Break this problem into two subproblems by setting (X + 0.3956043956) equal to 0.743039187 and -0.743039187.Subproblem 1
X + 0.3956043956 = 0.743039187 Simplifying X + 0.3956043956 = 0.743039187 Reorder the terms: 0.3956043956 + X = 0.743039187 Solving 0.3956043956 + X = 0.743039187 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.3956043956' to each side of the equation. 0.3956043956 + -0.3956043956 + X = 0.743039187 + -0.3956043956 Combine like terms: 0.3956043956 + -0.3956043956 = 0.0000000000 0.0000000000 + X = 0.743039187 + -0.3956043956 X = 0.743039187 + -0.3956043956 Combine like terms: 0.743039187 + -0.3956043956 = 0.3474347914 X = 0.3474347914 Simplifying X = 0.3474347914Subproblem 2
X + 0.3956043956 = -0.743039187 Simplifying X + 0.3956043956 = -0.743039187 Reorder the terms: 0.3956043956 + X = -0.743039187 Solving 0.3956043956 + X = -0.743039187 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.3956043956' to each side of the equation. 0.3956043956 + -0.3956043956 + X = -0.743039187 + -0.3956043956 Combine like terms: 0.3956043956 + -0.3956043956 = 0.0000000000 0.0000000000 + X = -0.743039187 + -0.3956043956 X = -0.743039187 + -0.3956043956 Combine like terms: -0.743039187 + -0.3956043956 = -1.1386435826 X = -1.1386435826 Simplifying X = -1.1386435826Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.3474347914, -1.1386435826}
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