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Simplifying (x + 4)(x + -3) = 16 Reorder the terms: (4 + x)(x + -3) = 16 Reorder the terms: (4 + x)(-3 + x) = 16 Multiply (4 + x) * (-3 + x) (4(-3 + x) + x(-3 + x)) = 16 ((-3 * 4 + x * 4) + x(-3 + x)) = 16 ((-12 + 4x) + x(-3 + x)) = 16 (-12 + 4x + (-3 * x + x * x)) = 16 (-12 + 4x + (-3x + x2)) = 16 Combine like terms: 4x + -3x = 1x (-12 + 1x + x2) = 16 Solving -12 + 1x + x2 = 16 Solving for variable 'x'. Reorder the terms: -12 + -16 + 1x + x2 = 16 + -16 Combine like terms: -12 + -16 = -28 -28 + 1x + x2 = 16 + -16 Combine like terms: 16 + -16 = 0 -28 + 1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '28' to each side of the equation. -28 + 1x + 28 + x2 = 0 + 28 Reorder the terms: -28 + 28 + 1x + x2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + 1x + x2 = 0 + 28 1x + x2 = 0 + 28 Combine like terms: 0 + 28 = 28 1x + x2 = 28 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 = 28 + 0.25 Reorder the terms: 0.25 + x + x2 = 28 + 0.25 Combine like terms: 28 + 0.25 = 28.25 0.25 + x + x2 = 28.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 28.25 Calculate the square root of the right side: 5.315072906 Break this problem into two subproblems by setting (x + 0.5) equal to 5.315072906 and -5.315072906.Subproblem 1
x + 0.5 = 5.315072906 Simplifying x + 0.5 = 5.315072906 Reorder the terms: 0.5 + x = 5.315072906 Solving 0.5 + x = 5.315072906 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 = 5.315072906 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 5.315072906 + -0.5 x = 5.315072906 + -0.5 Combine like terms: 5.315072906 + -0.5 = 4.815072906 x = 4.815072906 Simplifying x = 4.815072906Subproblem 2
x + 0.5 = -5.315072906 Simplifying x + 0.5 = -5.315072906 Reorder the terms: 0.5 + x = -5.315072906 Solving 0.5 + x = -5.315072906 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 = -5.315072906 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -5.315072906 + -0.5 x = -5.315072906 + -0.5 Combine like terms: -5.315072906 + -0.5 = -5.815072906 x = -5.815072906 Simplifying x = -5.815072906Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.815072906, -5.815072906}
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