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Simplifying (x + 2)(x + -3) = 5 Reorder the terms: (2 + x)(x + -3) = 5 Reorder the terms: (2 + x)(-3 + x) = 5 Multiply (2 + x) * (-3 + x) (2(-3 + x) + x(-3 + x)) = 5 ((-3 * 2 + x * 2) + x(-3 + x)) = 5 ((-6 + 2x) + x(-3 + x)) = 5 (-6 + 2x + (-3 * x + x * x)) = 5 (-6 + 2x + (-3x + x2)) = 5 Combine like terms: 2x + -3x = -1x (-6 + -1x + x2) = 5 Solving -6 + -1x + x2 = 5 Solving for variable 'x'. Reorder the terms: -6 + -5 + -1x + x2 = 5 + -5 Combine like terms: -6 + -5 = -11 -11 + -1x + x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -11 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + -1x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + -1x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -1x + x2 = 0 + 11 -1x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 -1x + x2 = 11 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 11 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 11 + 0.25 Combine like terms: 11 + 0.25 = 11.25 0.25 + -1x + x2 = 11.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 11.25 Calculate the square root of the right side: 3.354101966 Break this problem into two subproblems by setting (x + -0.5) equal to 3.354101966 and -3.354101966.Subproblem 1
x + -0.5 = 3.354101966 Simplifying x + -0.5 = 3.354101966 Reorder the terms: -0.5 + x = 3.354101966 Solving -0.5 + x = 3.354101966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 3.354101966 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 3.354101966 + 0.5 x = 3.354101966 + 0.5 Combine like terms: 3.354101966 + 0.5 = 3.854101966 x = 3.854101966 Simplifying x = 3.854101966Subproblem 2
x + -0.5 = -3.354101966 Simplifying x + -0.5 = -3.354101966 Reorder the terms: -0.5 + x = -3.354101966 Solving -0.5 + x = -3.354101966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -3.354101966 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -3.354101966 + 0.5 x = -3.354101966 + 0.5 Combine like terms: -3.354101966 + 0.5 = -2.854101966 x = -2.854101966 Simplifying x = -2.854101966Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.854101966, -2.854101966}
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