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Simplifying 24x + 48 + 24x = x2 + 2x Reorder the terms: 48 + 24x + 24x = x2 + 2x Combine like terms: 24x + 24x = 48x 48 + 48x = x2 + 2x Reorder the terms: 48 + 48x = 2x + x2 Solving 48 + 48x = 2x + x2 Solving for variable 'x'. Combine like terms: 48x + -2x = 46x 48 + 46x + -1x2 = 2x + x2 + -2x + -1x2 Reorder the terms: 48 + 46x + -1x2 = 2x + -2x + x2 + -1x2 Combine like terms: 2x + -2x = 0 48 + 46x + -1x2 = 0 + x2 + -1x2 48 + 46x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 48 + 46x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -48 + -46x + x2 = 0 Move the constant term to the right: Add '48' to each side of the equation. -48 + -46x + 48 + x2 = 0 + 48 Reorder the terms: -48 + 48 + -46x + x2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + -46x + x2 = 0 + 48 -46x + x2 = 0 + 48 Combine like terms: 0 + 48 = 48 -46x + x2 = 48 The x term is -46x. Take half its coefficient (-23). Square it (529) and add it to both sides. Add '529' to each side of the equation. -46x + 529 + x2 = 48 + 529 Reorder the terms: 529 + -46x + x2 = 48 + 529 Combine like terms: 48 + 529 = 577 529 + -46x + x2 = 577 Factor a perfect square on the left side: (x + -23)(x + -23) = 577 Calculate the square root of the right side: 24.020824299 Break this problem into two subproblems by setting (x + -23) equal to 24.020824299 and -24.020824299.Subproblem 1
x + -23 = 24.020824299 Simplifying x + -23 = 24.020824299 Reorder the terms: -23 + x = 24.020824299 Solving -23 + x = 24.020824299 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '23' to each side of the equation. -23 + 23 + x = 24.020824299 + 23 Combine like terms: -23 + 23 = 0 0 + x = 24.020824299 + 23 x = 24.020824299 + 23 Combine like terms: 24.020824299 + 23 = 47.020824299 x = 47.020824299 Simplifying x = 47.020824299Subproblem 2
x + -23 = -24.020824299 Simplifying x + -23 = -24.020824299 Reorder the terms: -23 + x = -24.020824299 Solving -23 + x = -24.020824299 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '23' to each side of the equation. -23 + 23 + x = -24.020824299 + 23 Combine like terms: -23 + 23 = 0 0 + x = -24.020824299 + 23 x = -24.020824299 + 23 Combine like terms: -24.020824299 + 23 = -1.020824299 x = -1.020824299 Simplifying x = -1.020824299Solution
The solution to the problem is based on the solutions from the subproblems. x = {47.020824299, -1.020824299}
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