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Simplifying 20x2 + 108x + 40 = 9 Reorder the terms: 40 + 108x + 20x2 = 9 Solving 40 + 108x + 20x2 = 9 Solving for variable 'x'. Reorder the terms: 40 + -9 + 108x + 20x2 = 9 + -9 Combine like terms: 40 + -9 = 31 31 + 108x + 20x2 = 9 + -9 Combine like terms: 9 + -9 = 0 31 + 108x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. 1.55 + 5.4x + x2 = 0 Move the constant term to the right: Add '-1.55' to each side of the equation. 1.55 + 5.4x + -1.55 + x2 = 0 + -1.55 Reorder the terms: 1.55 + -1.55 + 5.4x + x2 = 0 + -1.55 Combine like terms: 1.55 + -1.55 = 0.00 0.00 + 5.4x + x2 = 0 + -1.55 5.4x + x2 = 0 + -1.55 Combine like terms: 0 + -1.55 = -1.55 5.4x + x2 = -1.55 The x term is 5.4x. Take half its coefficient (2.7). Square it (7.29) and add it to both sides. Add '7.29' to each side of the equation. 5.4x + 7.29 + x2 = -1.55 + 7.29 Reorder the terms: 7.29 + 5.4x + x2 = -1.55 + 7.29 Combine like terms: -1.55 + 7.29 = 5.74 7.29 + 5.4x + x2 = 5.74 Factor a perfect square on the left side: (x + 2.7)(x + 2.7) = 5.74 Calculate the square root of the right side: 2.39582971 Break this problem into two subproblems by setting (x + 2.7) equal to 2.39582971 and -2.39582971.Subproblem 1
x + 2.7 = 2.39582971 Simplifying x + 2.7 = 2.39582971 Reorder the terms: 2.7 + x = 2.39582971 Solving 2.7 + x = 2.39582971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.7' to each side of the equation. 2.7 + -2.7 + x = 2.39582971 + -2.7 Combine like terms: 2.7 + -2.7 = 0.0 0.0 + x = 2.39582971 + -2.7 x = 2.39582971 + -2.7 Combine like terms: 2.39582971 + -2.7 = -0.30417029 x = -0.30417029 Simplifying x = -0.30417029Subproblem 2
x + 2.7 = -2.39582971 Simplifying x + 2.7 = -2.39582971 Reorder the terms: 2.7 + x = -2.39582971 Solving 2.7 + x = -2.39582971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.7' to each side of the equation. 2.7 + -2.7 + x = -2.39582971 + -2.7 Combine like terms: 2.7 + -2.7 = 0.0 0.0 + x = -2.39582971 + -2.7 x = -2.39582971 + -2.7 Combine like terms: -2.39582971 + -2.7 = -5.09582971 x = -5.09582971 Simplifying x = -5.09582971Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.30417029, -5.09582971}
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