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Simplifying (x + -2)(x + 3) = 16 Reorder the terms: (-2 + x)(x + 3) = 16 Reorder the terms: (-2 + x)(3 + x) = 16 Multiply (-2 + x) * (3 + x) (-2(3 + x) + x(3 + x)) = 16 ((3 * -2 + x * -2) + x(3 + x)) = 16 ((-6 + -2x) + x(3 + x)) = 16 (-6 + -2x + (3 * x + x * x)) = 16 (-6 + -2x + (3x + x2)) = 16 Combine like terms: -2x + 3x = 1x (-6 + 1x + x2) = 16 Solving -6 + 1x + x2 = 16 Solving for variable 'x'. Reorder the terms: -6 + -16 + 1x + x2 = 16 + -16 Combine like terms: -6 + -16 = -22 -22 + 1x + x2 = 16 + -16 Combine like terms: 16 + -16 = 0 -22 + 1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '22' to each side of the equation. -22 + 1x + 22 + x2 = 0 + 22 Reorder the terms: -22 + 22 + 1x + x2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + 1x + x2 = 0 + 22 1x + x2 = 0 + 22 Combine like terms: 0 + 22 = 22 1x + x2 = 22 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. x + 0.25 + x2 = 22 + 0.25 Reorder the terms: 0.25 + x + x2 = 22 + 0.25 Combine like terms: 22 + 0.25 = 22.25 0.25 + x + x2 = 22.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 22.25 Calculate the square root of the right side: 4.716990566 Break this problem into two subproblems by setting (x + 0.5) equal to 4.716990566 and -4.716990566.Subproblem 1
x + 0.5 = 4.716990566 Simplifying x + 0.5 = 4.716990566 Reorder the terms: 0.5 + x = 4.716990566 Solving 0.5 + x = 4.716990566 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 = 4.716990566 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 4.716990566 + -0.5 x = 4.716990566 + -0.5 Combine like terms: 4.716990566 + -0.5 = 4.216990566 x = 4.216990566 Simplifying x = 4.216990566Subproblem 2
x + 0.5 = -4.716990566 Simplifying x + 0.5 = -4.716990566 Reorder the terms: 0.5 + x = -4.716990566 Solving 0.5 + x = -4.716990566 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 = -4.716990566 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -4.716990566 + -0.5 x = -4.716990566 + -0.5 Combine like terms: -4.716990566 + -0.5 = -5.216990566 x = -5.216990566 Simplifying x = -5.216990566Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.216990566, -5.216990566}
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