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Simplifying (x + -1)(x + 4) = 7 Reorder the terms: (-1 + x)(x + 4) = 7 Reorder the terms: (-1 + x)(4 + x) = 7 Multiply (-1 + x) * (4 + x) (-1(4 + x) + x(4 + x)) = 7 ((4 * -1 + x * -1) + x(4 + x)) = 7 ((-4 + -1x) + x(4 + x)) = 7 (-4 + -1x + (4 * x + x * x)) = 7 (-4 + -1x + (4x + x2)) = 7 Combine like terms: -1x + 4x = 3x (-4 + 3x + x2) = 7 Solving -4 + 3x + x2 = 7 Solving for variable 'x'. Reorder the terms: -4 + -7 + 3x + x2 = 7 + -7 Combine like terms: -4 + -7 = -11 -11 + 3x + x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -11 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + 3x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + 3x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 3x + x2 = 0 + 11 3x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 3x + x2 = 11 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 = 11 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 11 + 2.25 Combine like terms: 11 + 2.25 = 13.25 2.25 + 3x + x2 = 13.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 13.25 Calculate the square root of the right side: 3.640054945 Break this problem into two subproblems by setting (x + 1.5) equal to 3.640054945 and -3.640054945.Subproblem 1
x + 1.5 = 3.640054945 Simplifying x + 1.5 = 3.640054945 Reorder the terms: 1.5 + x = 3.640054945 Solving 1.5 + x = 3.640054945 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 = 3.640054945 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 3.640054945 + -1.5 x = 3.640054945 + -1.5 Combine like terms: 3.640054945 + -1.5 = 2.140054945 x = 2.140054945 Simplifying x = 2.140054945Subproblem 2
x + 1.5 = -3.640054945 Simplifying x + 1.5 = -3.640054945 Reorder the terms: 1.5 + x = -3.640054945 Solving 1.5 + x = -3.640054945 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 = -3.640054945 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -3.640054945 + -1.5 x = -3.640054945 + -1.5 Combine like terms: -3.640054945 + -1.5 = -5.140054945 x = -5.140054945 Simplifying x = -5.140054945Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.140054945, -5.140054945}
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