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Simplifying x(x + 3) = 164 Reorder the terms: x(3 + x) = 164 (3 * x + x * x) = 164 (3x + x2) = 164 Solving 3x + x2 = 164 Solving for variable 'x'. Reorder the terms: -164 + 3x + x2 = 164 + -164 Combine like terms: 164 + -164 = 0 -164 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '164' to each side of the equation. -164 + 3x + 164 + x2 = 0 + 164 Reorder the terms: -164 + 164 + 3x + x2 = 0 + 164 Combine like terms: -164 + 164 = 0 0 + 3x + x2 = 0 + 164 3x + x2 = 0 + 164 Combine like terms: 0 + 164 = 164 3x + x2 = 164 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 = 164 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 164 + 2.25 Combine like terms: 164 + 2.25 = 166.25 2.25 + 3x + x2 = 166.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 166.25 Calculate the square root of the right side: 12.893796958 Break this problem into two subproblems by setting (x + 1.5) equal to 12.893796958 and -12.893796958.Subproblem 1
x + 1.5 = 12.893796958 Simplifying x + 1.5 = 12.893796958 Reorder the terms: 1.5 + x = 12.893796958 Solving 1.5 + x = 12.893796958 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 = 12.893796958 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 12.893796958 + -1.5 x = 12.893796958 + -1.5 Combine like terms: 12.893796958 + -1.5 = 11.393796958 x = 11.393796958 Simplifying x = 11.393796958Subproblem 2
x + 1.5 = -12.893796958 Simplifying x + 1.5 = -12.893796958 Reorder the terms: 1.5 + x = -12.893796958 Solving 1.5 + x = -12.893796958 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 = -12.893796958 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -12.893796958 + -1.5 x = -12.893796958 + -1.5 Combine like terms: -12.893796958 + -1.5 = -14.393796958 x = -14.393796958 Simplifying x = -14.393796958Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.393796958, -14.393796958}
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