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Simplifying (x + 3) + -1(x + 2)(x + 2) = 5 Reorder the terms: (3 + x) + -1(x + 2)(x + 2) = 5 Remove parenthesis around (3 + x) 3 + x + -1(x + 2)(x + 2) = 5 Reorder the terms: 3 + x + -1(2 + x)(x + 2) = 5 Reorder the terms: 3 + x + -1(2 + x)(2 + x) = 5 Multiply (2 + x) * (2 + x) 3 + x + -1(2(2 + x) + x(2 + x)) = 5 3 + x + -1((2 * 2 + x * 2) + x(2 + x)) = 5 3 + x + -1((4 + 2x) + x(2 + x)) = 5 3 + x + -1(4 + 2x + (2 * x + x * x)) = 5 3 + x + -1(4 + 2x + (2x + x2)) = 5 Combine like terms: 2x + 2x = 4x 3 + x + -1(4 + 4x + x2) = 5 3 + x + (4 * -1 + 4x * -1 + x2 * -1) = 5 3 + x + (-4 + -4x + -1x2) = 5 Reorder the terms: 3 + -4 + x + -4x + -1x2 = 5 Combine like terms: 3 + -4 = -1 -1 + x + -4x + -1x2 = 5 Combine like terms: x + -4x = -3x -1 + -3x + -1x2 = 5 Solving -1 + -3x + -1x2 = 5 Solving for variable 'x'. Reorder the terms: -1 + -5 + -3x + -1x2 = 5 + -5 Combine like terms: -1 + -5 = -6 -6 + -3x + -1x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -6 + -3x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(6 + 3x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(6 + 3x + x2)' equal to zero and attempt to solve: Simplifying 6 + 3x + x2 = 0 Solving 6 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + 3x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + 3x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 3x + x2 = 0 + -6 3x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 3x + x2 = -6 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 = -6 + 2.25 Reorder the terms: 2.25 + 3x + x2 = -6 + 2.25 Combine like terms: -6 + 2.25 = -3.75 2.25 + 3x + x2 = -3.75 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = -3.75 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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