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Simplifying 6x2 + -12x + -23 = 0 Reorder the terms: -23 + -12x + 6x2 = 0 Solving -23 + -12x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -3.833333333 + -2x + x2 = 0 Move the constant term to the right: Add '3.833333333' to each side of the equation. -3.833333333 + -2x + 3.833333333 + x2 = 0 + 3.833333333 Reorder the terms: -3.833333333 + 3.833333333 + -2x + x2 = 0 + 3.833333333 Combine like terms: -3.833333333 + 3.833333333 = 0.000000000 0.000000000 + -2x + x2 = 0 + 3.833333333 -2x + x2 = 0 + 3.833333333 Combine like terms: 0 + 3.833333333 = 3.833333333 -2x + x2 = 3.833333333 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 3.833333333 + 1 Reorder the terms: 1 + -2x + x2 = 3.833333333 + 1 Combine like terms: 3.833333333 + 1 = 4.833333333 1 + -2x + x2 = 4.833333333 Factor a perfect square on the left side: (x + -1)(x + -1) = 4.833333333 Calculate the square root of the right side: 2.198484326 Break this problem into two subproblems by setting (x + -1) equal to 2.198484326 and -2.198484326.Subproblem 1
x + -1 = 2.198484326 Simplifying x + -1 = 2.198484326 Reorder the terms: -1 + x = 2.198484326 Solving -1 + x = 2.198484326 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 2.198484326 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.198484326 + 1 x = 2.198484326 + 1 Combine like terms: 2.198484326 + 1 = 3.198484326 x = 3.198484326 Simplifying x = 3.198484326Subproblem 2
x + -1 = -2.198484326 Simplifying x + -1 = -2.198484326 Reorder the terms: -1 + x = -2.198484326 Solving -1 + x = -2.198484326 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -2.198484326 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.198484326 + 1 x = -2.198484326 + 1 Combine like terms: -2.198484326 + 1 = -1.198484326 x = -1.198484326 Simplifying x = -1.198484326Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.198484326, -1.198484326}
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