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Simplifying (x + 2)(x + 1) = 24.75 Reorder the terms: (2 + x)(x + 1) = 24.75 Reorder the terms: (2 + x)(1 + x) = 24.75 Multiply (2 + x) * (1 + x) (2(1 + x) + x(1 + x)) = 24.75 ((1 * 2 + x * 2) + x(1 + x)) = 24.75 ((2 + 2x) + x(1 + x)) = 24.75 (2 + 2x + (1 * x + x * x)) = 24.75 (2 + 2x + (1x + x2)) = 24.75 Combine like terms: 2x + 1x = 3x (2 + 3x + x2) = 24.75 Solving 2 + 3x + x2 = 24.75 Solving for variable 'x'. Reorder the terms: 2 + -24.75 + 3x + x2 = 24.75 + -24.75 Combine like terms: 2 + -24.75 = -22.75 -22.75 + 3x + x2 = 24.75 + -24.75 Combine like terms: 24.75 + -24.75 = 0.00 -22.75 + 3x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '22.75' to each side of the equation. -22.75 + 3x + 22.75 + x2 = 0.00 + 22.75 Reorder the terms: -22.75 + 22.75 + 3x + x2 = 0.00 + 22.75 Combine like terms: -22.75 + 22.75 = 0.00 0.00 + 3x + x2 = 0.00 + 22.75 3x + x2 = 0.00 + 22.75 Combine like terms: 0.00 + 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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