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Simplifying (x + 5)(x + -2) = 3 Reorder the terms: (5 + x)(x + -2) = 3 Reorder the terms: (5 + x)(-2 + x) = 3 Multiply (5 + x) * (-2 + x) (5(-2 + x) + x(-2 + x)) = 3 ((-2 * 5 + x * 5) + x(-2 + x)) = 3 ((-10 + 5x) + x(-2 + x)) = 3 (-10 + 5x + (-2 * x + x * x)) = 3 (-10 + 5x + (-2x + x2)) = 3 Combine like terms: 5x + -2x = 3x (-10 + 3x + x2) = 3 Solving -10 + 3x + x2 = 3 Solving for variable 'x'. Reorder the terms: -10 + -3 + 3x + x2 = 3 + -3 Combine like terms: -10 + -3 = -13 -13 + 3x + x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -13 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + 3x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + 3x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 3x + x2 = 0 + 13 3x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 3x + x2 = 13 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 = 13 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 13 + 2.25 Combine like terms: 13 + 2.25 = 15.25 2.25 + 3x + x2 = 15.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 15.25 Calculate the square root of the right side: 3.905124838 Break this problem into two subproblems by setting (x + 1.5) equal to 3.905124838 and -3.905124838.Subproblem 1
x + 1.5 = 3.905124838 Simplifying x + 1.5 = 3.905124838 Reorder the terms: 1.5 + x = 3.905124838 Solving 1.5 + x = 3.905124838 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 = 3.905124838 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 3.905124838 + -1.5 x = 3.905124838 + -1.5 Combine like terms: 3.905124838 + -1.5 = 2.405124838 x = 2.405124838 Simplifying x = 2.405124838Subproblem 2
x + 1.5 = -3.905124838 Simplifying x + 1.5 = -3.905124838 Reorder the terms: 1.5 + x = -3.905124838 Solving 1.5 + x = -3.905124838 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 = -3.905124838 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -3.905124838 + -1.5 x = -3.905124838 + -1.5 Combine like terms: -3.905124838 + -1.5 = -5.405124838 x = -5.405124838 Simplifying x = -5.405124838Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.405124838, -5.405124838}
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