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Simplifying 9x2 = 3 + -2x Solving 9x2 = 3 + -2x Solving for variable 'x'. Reorder the terms: -3 + 2x + 9x2 = 3 + -2x + -3 + 2x Reorder the terms: -3 + 2x + 9x2 = 3 + -3 + -2x + 2x Combine like terms: 3 + -3 = 0 -3 + 2x + 9x2 = 0 + -2x + 2x -3 + 2x + 9x2 = -2x + 2x Combine like terms: -2x + 2x = 0 -3 + 2x + 9x2 = 0 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 = 0.4768336249 x = 0.4768336249 Simplifying x = 0.4768336249Subproblem 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 = -0.6990558471 x = -0.6990558471 Simplifying x = -0.6990558471Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4768336249, -0.6990558471}
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