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Simplifying (x + 2)(x + 3) = 100 Reorder the terms: (2 + x)(x + 3) = 100 Reorder the terms: (2 + x)(3 + x) = 100 Multiply (2 + x) * (3 + x) (2(3 + x) + x(3 + x)) = 100 ((3 * 2 + x * 2) + x(3 + x)) = 100 ((6 + 2x) + x(3 + x)) = 100 (6 + 2x + (3 * x + x * x)) = 100 (6 + 2x + (3x + x2)) = 100 Combine like terms: 2x + 3x = 5x (6 + 5x + x2) = 100 Solving 6 + 5x + x2 = 100 Solving for variable 'x'. Reorder the terms: 6 + -100 + 5x + x2 = 100 + -100 Combine like terms: 6 + -100 = -94 -94 + 5x + x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -94 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '94' to each side of the equation. -94 + 5x + 94 + x2 = 0 + 94 Reorder the terms: -94 + 94 + 5x + x2 = 0 + 94 Combine like terms: -94 + 94 = 0 0 + 5x + x2 = 0 + 94 5x + x2 = 0 + 94 Combine like terms: 0 + 94 = 94 5x + x2 = 94 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 94 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 94 + 6.25 Combine like terms: 94 + 6.25 = 100.25 6.25 + 5x + x2 = 100.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 100.25 Calculate the square root of the right side: 10.012492197 Break this problem into two subproblems by setting (x + 2.5) equal to 10.012492197 and -10.012492197.Subproblem 1
x + 2.5 = 10.012492197 Simplifying x + 2.5 = 10.012492197 Reorder the terms: 2.5 + x = 10.012492197 Solving 2.5 + x = 10.012492197 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 10.012492197 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 10.012492197 + -2.5 x = 10.012492197 + -2.5 Combine like terms: 10.012492197 + -2.5 = 7.512492197 x = 7.512492197 Simplifying x = 7.512492197Subproblem 2
x + 2.5 = -10.012492197 Simplifying x + 2.5 = -10.012492197 Reorder the terms: 2.5 + x = -10.012492197 Solving 2.5 + x = -10.012492197 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -10.012492197 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -10.012492197 + -2.5 x = -10.012492197 + -2.5 Combine like terms: -10.012492197 + -2.5 = -12.512492197 x = -12.512492197 Simplifying x = -12.512492197Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.512492197, -12.512492197}
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