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Simplifying (32x2 + 2x + 18x) + (18 + 12x + 39x) = 0 Reorder the terms: (2x + 18x + 32x2) + (18 + 12x + 39x) = 0 Combine like terms: 2x + 18x = 20x (20x + 32x2) + (18 + 12x + 39x) = 0 Remove parenthesis around (20x + 32x2) 20x + 32x2 + (18 + 12x + 39x) = 0 Combine like terms: 12x + 39x = 51x 20x + 32x2 + (18 + 51x) = 0 Remove parenthesis around (18 + 51x) 20x + 32x2 + 18 + 51x = 0 Reorder the terms: 18 + 20x + 51x + 32x2 = 0 Combine like terms: 20x + 51x = 71x 18 + 71x + 32x2 = 0 Solving 18 + 71x + 32x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. 0.5625 + 2.21875x + x2 = 0 Move the constant term to the right: Add '-0.5625' to each side of the equation. 0.5625 + 2.21875x + -0.5625 + x2 = 0 + -0.5625 Reorder the terms: 0.5625 + -0.5625 + 2.21875x + x2 = 0 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + 2.21875x + x2 = 0 + -0.5625 2.21875x + x2 = 0 + -0.5625 Combine like terms: 0 + -0.5625 = -0.5625 2.21875x + x2 = -0.5625 The x term is 2.21875x. Take half its coefficient (1.109375). Square it (1.230712891) and add it to both sides. Add '1.230712891' to each side of the equation. 2.21875x + 1.230712891 + x2 = -0.5625 + 1.230712891 Reorder the terms: 1.230712891 + 2.21875x + x2 = -0.5625 + 1.230712891 Combine like terms: -0.5625 + 1.230712891 = 0.668212891 1.230712891 + 2.21875x + x2 = 0.668212891 Factor a perfect square on the left side: (x + 1.109375)(x + 1.109375) = 0.668212891 Calculate the square root of the right side: 0.817442898 Break this problem into two subproblems by setting (x + 1.109375) equal to 0.817442898 and -0.817442898.Subproblem 1
x + 1.109375 = 0.817442898 Simplifying x + 1.109375 = 0.817442898 Reorder the terms: 1.109375 + x = 0.817442898 Solving 1.109375 + x = 0.817442898 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.109375' to each side of the equation. 1.109375 + -1.109375 + x = 0.817442898 + -1.109375 Combine like terms: 1.109375 + -1.109375 = 0.000000 0.000000 + x = 0.817442898 + -1.109375 x = 0.817442898 + -1.109375 Combine like terms: 0.817442898 + -1.109375 = -0.291932102 x = -0.291932102 Simplifying x = -0.291932102Subproblem 2
x + 1.109375 = -0.817442898 Simplifying x + 1.109375 = -0.817442898 Reorder the terms: 1.109375 + x = -0.817442898 Solving 1.109375 + x = -0.817442898 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.109375' to each side of the equation. 1.109375 + -1.109375 + x = -0.817442898 + -1.109375 Combine like terms: 1.109375 + -1.109375 = 0.000000 0.000000 + x = -0.817442898 + -1.109375 x = -0.817442898 + -1.109375 Combine like terms: -0.817442898 + -1.109375 = -1.926817898 x = -1.926817898 Simplifying x = -1.926817898Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.291932102, -1.926817898}
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