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Simplifying 24.75 = x2 + 3x + 2 Reorder the terms: 24.75 = 2 + 3x + x2 Solving 24.75 = 2 + 3x + x2 Solving for variable 'x'. Combine like terms: 24.75 + -2 = 22.75 22.75 + -3x + -1x2 = 2 + 3x + x2 + -2 + -3x + -1x2 Reorder the terms: 22.75 + -3x + -1x2 = 2 + -2 + 3x + -3x + x2 + -1x2 Combine like terms: 2 + -2 = 0 22.75 + -3x + -1x2 = 0 + 3x + -3x + x2 + -1x2 22.75 + -3x + -1x2 = 3x + -3x + x2 + -1x2 Combine like terms: 3x + -3x = 0 22.75 + -3x + -1x2 = 0 + x2 + -1x2 22.75 + -3x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 22.75 + -3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -22.75 + 3x + x2 = 0 Move the constant term to the right: Add '22.75' to each side of the equation. -22.75 + 3x + 22.75 + x2 = 0 + 22.75 Reorder the terms: -22.75 + 22.75 + 3x + x2 = 0 + 22.75 Combine like terms: -22.75 + 22.75 = 0.00 0.00 + 3x + x2 = 0 + 22.75 3x + x2 = 0 + 22.75 Combine like terms: 0 + 22.75 = 22.75 3x + x2 = 22.75 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 22.75 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 22.75 + 2.25 Combine like terms: 22.75 + 2.25 = 25 2.25 + 3x + x2 = 25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 25 Calculate the square root of the right side: 5 Break this problem into two subproblems by setting (x + 1.5) equal to 5 and -5.Subproblem 1
x + 1.5 = 5 Simplifying x + 1.5 = 5 Reorder the terms: 1.5 + x = 5 Solving 1.5 + x = 5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 5 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 5 + -1.5 x = 5 + -1.5 Combine like terms: 5 + -1.5 = 3.5 x = 3.5 Simplifying x = 3.5Subproblem 2
x + 1.5 = -5 Simplifying x + 1.5 = -5 Reorder the terms: 1.5 + x = -5 Solving 1.5 + x = -5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -5 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -5 + -1.5 x = -5 + -1.5 Combine like terms: -5 + -1.5 = -6.5 x = -6.5 Simplifying x = -6.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.5, -6.5}
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