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Simplifying (x + -1)(x + 4) = 9 Reorder the terms: (-1 + x)(x + 4) = 9 Reorder the terms: (-1 + x)(4 + x) = 9 Multiply (-1 + x) * (4 + x) (-1(4 + x) + x(4 + x)) = 9 ((4 * -1 + x * -1) + x(4 + x)) = 9 ((-4 + -1x) + x(4 + x)) = 9 (-4 + -1x + (4 * x + x * x)) = 9 (-4 + -1x + (4x + x2)) = 9 Combine like terms: -1x + 4x = 3x (-4 + 3x + x2) = 9 Solving -4 + 3x + x2 = 9 Solving for variable 'x'. Reorder the terms: -4 + -9 + 3x + x2 = 9 + -9 Combine like terms: -4 + -9 = -13 -13 + 3x + x2 = 9 + -9 Combine like terms: 9 + -9 = 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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