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Simplifying (x + 3)(x) = 75 Reorder the terms: (3 + x)(x) = 75 Reorder the terms for easier multiplication: x(3 + x) = 75 (3 * x + x * x) = 75 (3x + x2) = 75 Solving 3x + x2 = 75 Solving for variable 'x'. Reorder the terms: -75 + 3x + x2 = 75 + -75 Combine like terms: 75 + -75 = 0 -75 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '75' to each side of the equation. -75 + 3x + 75 + x2 = 0 + 75 Reorder the terms: -75 + 75 + 3x + x2 = 0 + 75 Combine like terms: -75 + 75 = 0 0 + 3x + x2 = 0 + 75 3x + x2 = 0 + 75 Combine like terms: 0 + 75 = 75 3x + x2 = 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 = 75 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 75 + 2.25 Combine like terms: 75 + 2.25 = 77.25 2.25 + 3x + x2 = 77.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 77.25 Calculate the square root of the right side: 8.789197916 Break this problem into two subproblems by setting (x + 1.5) equal to 8.789197916 and -8.789197916.Subproblem 1
x + 1.5 = 8.789197916 Simplifying x + 1.5 = 8.789197916 Reorder the terms: 1.5 + x = 8.789197916 Solving 1.5 + x = 8.789197916 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 = 8.789197916 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 8.789197916 + -1.5 x = 8.789197916 + -1.5 Combine like terms: 8.789197916 + -1.5 = 7.289197916 x = 7.289197916 Simplifying x = 7.289197916Subproblem 2
x + 1.5 = -8.789197916 Simplifying x + 1.5 = -8.789197916 Reorder the terms: 1.5 + x = -8.789197916 Solving 1.5 + x = -8.789197916 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 = -8.789197916 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -8.789197916 + -1.5 x = -8.789197916 + -1.5 Combine like terms: -8.789197916 + -1.5 = -10.289197916 x = -10.289197916 Simplifying x = -10.289197916Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.289197916, -10.289197916}
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