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Simplifying 23x2 + 18x + -3 = 0 Reorder the terms: -3 + 18x + 23x2 = 0 Solving -3 + 18x + 23x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 23 the coefficient of the squared term: Divide each side by '23'. -0.1304347826 + 0.7826086957x + x2 = 0 Move the constant term to the right: Add '0.1304347826' to each side of the equation. -0.1304347826 + 0.7826086957x + 0.1304347826 + x2 = 0 + 0.1304347826 Reorder the terms: -0.1304347826 + 0.1304347826 + 0.7826086957x + x2 = 0 + 0.1304347826 Combine like terms: -0.1304347826 + 0.1304347826 = 0.0000000000 0.0000000000 + 0.7826086957x + x2 = 0 + 0.1304347826 0.7826086957x + x2 = 0 + 0.1304347826 Combine like terms: 0 + 0.1304347826 = 0.1304347826 0.7826086957x + x2 = 0.1304347826 The x term is 0.7826086957x. Take half its coefficient (0.3913043479). Square it (0.1531190927) and add it to both sides. Add '0.1531190927' to each side of the equation. 0.7826086957x + 0.1531190927 + x2 = 0.1304347826 + 0.1531190927 Reorder the terms: 0.1531190927 + 0.7826086957x + x2 = 0.1304347826 + 0.1531190927 Combine like terms: 0.1304347826 + 0.1531190927 = 0.2835538753 0.1531190927 + 0.7826086957x + x2 = 0.2835538753 Factor a perfect square on the left side: (x + 0.3913043479)(x + 0.3913043479) = 0.2835538753 Calculate the square root of the right side: 0.53249777 Break this problem into two subproblems by setting (x + 0.3913043479) equal to 0.53249777 and -0.53249777.Subproblem 1
x + 0.3913043479 = 0.53249777 Simplifying x + 0.3913043479 = 0.53249777 Reorder the terms: 0.3913043479 + x = 0.53249777 Solving 0.3913043479 + x = 0.53249777 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3913043479' to each side of the equation. 0.3913043479 + -0.3913043479 + x = 0.53249777 + -0.3913043479 Combine like terms: 0.3913043479 + -0.3913043479 = 0.0000000000 0.0000000000 + x = 0.53249777 + -0.3913043479 x = 0.53249777 + -0.3913043479 Combine like terms: 0.53249777 + -0.3913043479 = 0.1411934221 x = 0.1411934221 Simplifying x = 0.1411934221Subproblem 2
x + 0.3913043479 = -0.53249777 Simplifying x + 0.3913043479 = -0.53249777 Reorder the terms: 0.3913043479 + x = -0.53249777 Solving 0.3913043479 + x = -0.53249777 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3913043479' to each side of the equation. 0.3913043479 + -0.3913043479 + x = -0.53249777 + -0.3913043479 Combine like terms: 0.3913043479 + -0.3913043479 = 0.0000000000 0.0000000000 + x = -0.53249777 + -0.3913043479 x = -0.53249777 + -0.3913043479 Combine like terms: -0.53249777 + -0.3913043479 = -0.9238021179 x = -0.9238021179 Simplifying x = -0.9238021179Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1411934221, -0.9238021179}
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