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Simplifying (6x2 + -3x + 2) + (3x2 + x + -5) = 0 Reorder the terms: (2 + -3x + 6x2) + (3x2 + x + -5) = 0 Remove parenthesis around (2 + -3x + 6x2) 2 + -3x + 6x2 + (3x2 + x + -5) = 0 Reorder the terms: 2 + -3x + 6x2 + (-5 + x + 3x2) = 0 Remove parenthesis around (-5 + x + 3x2) 2 + -3x + 6x2 + -5 + x + 3x2 = 0 Reorder the terms: 2 + -5 + -3x + x + 6x2 + 3x2 = 0 Combine like terms: 2 + -5 = -3 -3 + -3x + x + 6x2 + 3x2 = 0 Combine like terms: -3x + x = -2x -3 + -2x + 6x2 + 3x2 = 0 Combine like terms: 6x2 + 3x2 = 9x2 -3 + -2x + 9x2 = 0 Solving -3 + -2x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.3333333333 + -0.2222222222x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + -0.2222222222x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + -0.2222222222x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + -0.2222222222x + x2 = 0 + 0.3333333333 -0.2222222222x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 -0.2222222222x + x2 = 0.3333333333 The x term is -0.2222222222x. Take half its coefficient (-0.1111111111). Square it (0.01234567901) and add it to both sides. Add '0.01234567901' to each side of the equation. -0.2222222222x + 0.01234567901 + x2 = 0.3333333333 + 0.01234567901 Reorder the terms: 0.01234567901 + -0.2222222222x + x2 = 0.3333333333 + 0.01234567901 Combine like terms: 0.3333333333 + 0.01234567901 = 0.34567901231 0.01234567901 + -0.2222222222x + x2 = 0.34567901231 Factor a perfect square on the left side: (x + -0.1111111111)(x + -0.1111111111) = 0.34567901231 Calculate the square root of the right side: 0.587944736 Break this problem into two subproblems by setting (x + -0.1111111111) equal to 0.587944736 and -0.587944736.Subproblem 1
x + -0.1111111111 = 0.587944736 Simplifying x + -0.1111111111 = 0.587944736 Reorder the terms: -0.1111111111 + x = 0.587944736 Solving -0.1111111111 + x = 0.587944736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1111111111' to each side of the equation. -0.1111111111 + 0.1111111111 + x = 0.587944736 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + x = 0.587944736 + 0.1111111111 x = 0.587944736 + 0.1111111111 Combine like terms: 0.587944736 + 0.1111111111 = 0.6990558471 x = 0.6990558471 Simplifying x = 0.6990558471Subproblem 2
x + -0.1111111111 = -0.587944736 Simplifying x + -0.1111111111 = -0.587944736 Reorder the terms: -0.1111111111 + x = -0.587944736 Solving -0.1111111111 + x = -0.587944736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1111111111' to each side of the equation. -0.1111111111 + 0.1111111111 + x = -0.587944736 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + x = -0.587944736 + 0.1111111111 x = -0.587944736 + 0.1111111111 Combine like terms: -0.587944736 + 0.1111111111 = -0.4768336249 x = -0.4768336249 Simplifying x = -0.4768336249Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6990558471, -0.4768336249}
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