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Simplifying 2x2 = 19x + 23 Reorder the terms: 2x2 = 23 + 19x Solving 2x2 = 23 + 19x Solving for variable 'x'. Reorder the terms: -23 + -19x + 2x2 = 23 + 19x + -23 + -19x Reorder the terms: -23 + -19x + 2x2 = 23 + -23 + 19x + -19x Combine like terms: 23 + -23 = 0 -23 + -19x + 2x2 = 0 + 19x + -19x -23 + -19x + 2x2 = 19x + -19x Combine like terms: 19x + -19x = 0 -23 + -19x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -11.5 + -9.5x + x2 = 0 Move the constant term to the right: Add '11.5' to each side of the equation. -11.5 + -9.5x + 11.5 + x2 = 0 + 11.5 Reorder the terms: -11.5 + 11.5 + -9.5x + x2 = 0 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + -9.5x + x2 = 0 + 11.5 -9.5x + x2 = 0 + 11.5 Combine like terms: 0 + 11.5 = 11.5 -9.5x + x2 = 11.5 The x term is -9.5x. Take half its coefficient (-4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. -9.5x + 22.5625 + x2 = 11.5 + 22.5625 Reorder the terms: 22.5625 + -9.5x + x2 = 11.5 + 22.5625 Combine like terms: 11.5 + 22.5625 = 34.0625 22.5625 + -9.5x + x2 = 34.0625 Factor a perfect square on the left side: (x + -4.75)(x + -4.75) = 34.0625 Calculate the square root of the right side: 5.836308765 Break this problem into two subproblems by setting (x + -4.75) equal to 5.836308765 and -5.836308765.Subproblem 1
x + -4.75 = 5.836308765 Simplifying x + -4.75 = 5.836308765 Reorder the terms: -4.75 + x = 5.836308765 Solving -4.75 + x = 5.836308765 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + x = 5.836308765 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = 5.836308765 + 4.75 x = 5.836308765 + 4.75 Combine like terms: 5.836308765 + 4.75 = 10.586308765 x = 10.586308765 Simplifying x = 10.586308765Subproblem 2
x + -4.75 = -5.836308765 Simplifying x + -4.75 = -5.836308765 Reorder the terms: -4.75 + x = -5.836308765 Solving -4.75 + x = -5.836308765 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + x = -5.836308765 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = -5.836308765 + 4.75 x = -5.836308765 + 4.75 Combine like terms: -5.836308765 + 4.75 = -1.086308765 x = -1.086308765 Simplifying x = -1.086308765Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.586308765, -1.086308765}
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