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Simplifying (3x + 2)(3x + -2) + -9(x + 1) = -22 Reorder the terms: (2 + 3x)(3x + -2) + -9(x + 1) = -22 Reorder the terms: (2 + 3x)(-2 + 3x) + -9(x + 1) = -22 Multiply (2 + 3x) * (-2 + 3x) (2(-2 + 3x) + 3x * (-2 + 3x)) + -9(x + 1) = -22 ((-2 * 2 + 3x * 2) + 3x * (-2 + 3x)) + -9(x + 1) = -22 ((-4 + 6x) + 3x * (-2 + 3x)) + -9(x + 1) = -22 (-4 + 6x + (-2 * 3x + 3x * 3x)) + -9(x + 1) = -22 (-4 + 6x + (-6x + 9x2)) + -9(x + 1) = -22 Combine like terms: 6x + -6x = 0 (-4 + 0 + 9x2) + -9(x + 1) = -22 (-4 + 9x2) + -9(x + 1) = -22 Reorder the terms: -4 + 9x2 + -9(1 + x) = -22 -4 + 9x2 + (1 * -9 + x * -9) = -22 -4 + 9x2 + (-9 + -9x) = -22 Reorder the terms: -4 + -9 + -9x + 9x2 = -22 Combine like terms: -4 + -9 = -13 -13 + -9x + 9x2 = -22 Solving -13 + -9x + 9x2 = -22 Solving for variable 'x'. Reorder the terms: -13 + 22 + -9x + 9x2 = -22 + 22 Combine like terms: -13 + 22 = 9 9 + -9x + 9x2 = -22 + 22 Combine like terms: -22 + 22 = 0 9 + -9x + 9x2 = 0 Factor out the Greatest Common Factor (GCF), '9'. 9(1 + -1x + x2) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(1 + -1x + x2)' equal to zero and attempt to solve: Simplifying 1 + -1x + x2 = 0 Solving 1 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -1x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -1x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x + x2 = 0 + -1 -1x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -1x + x2 = -1 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. -1x + 0.25 + x2 = -1 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -1 + 0.25 Combine like terms: -1 + 0.25 = -0.75 0.25 + -1x + x2 = -0.75 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = -0.75 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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