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Simplifying 9(2x + 2) = (2x + 6)(2x + 6) Reorder the terms: 9(2 + 2x) = (2x + 6)(2x + 6) (2 * 9 + 2x * 9) = (2x + 6)(2x + 6) (18 + 18x) = (2x + 6)(2x + 6) Reorder the terms: 18 + 18x = (6 + 2x)(2x + 6) Reorder the terms: 18 + 18x = (6 + 2x)(6 + 2x) Multiply (6 + 2x) * (6 + 2x) 18 + 18x = (6(6 + 2x) + 2x * (6 + 2x)) 18 + 18x = ((6 * 6 + 2x * 6) + 2x * (6 + 2x)) 18 + 18x = ((36 + 12x) + 2x * (6 + 2x)) 18 + 18x = (36 + 12x + (6 * 2x + 2x * 2x)) 18 + 18x = (36 + 12x + (12x + 4x2)) Combine like terms: 12x + 12x = 24x 18 + 18x = (36 + 24x + 4x2) Solving 18 + 18x = 36 + 24x + 4x2 Solving for variable 'x'. Reorder the terms: 18 + -36 + 18x + -24x + -4x2 = 36 + 24x + 4x2 + -36 + -24x + -4x2 Combine like terms: 18 + -36 = -18 -18 + 18x + -24x + -4x2 = 36 + 24x + 4x2 + -36 + -24x + -4x2 Combine like terms: 18x + -24x = -6x -18 + -6x + -4x2 = 36 + 24x + 4x2 + -36 + -24x + -4x2 Reorder the terms: -18 + -6x + -4x2 = 36 + -36 + 24x + -24x + 4x2 + -4x2 Combine like terms: 36 + -36 = 0 -18 + -6x + -4x2 = 0 + 24x + -24x + 4x2 + -4x2 -18 + -6x + -4x2 = 24x + -24x + 4x2 + -4x2 Combine like terms: 24x + -24x = 0 -18 + -6x + -4x2 = 0 + 4x2 + -4x2 -18 + -6x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -18 + -6x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(9 + 3x + 2x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(9 + 3x + 2x2)' equal to zero and attempt to solve: Simplifying 9 + 3x + 2x2 = 0 Solving 9 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4.5 + 1.5x + x2 = 0 Move the constant term to the right: Add '-4.5' to each side of the equation. 4.5 + 1.5x + -4.5 + x2 = 0 + -4.5 Reorder the terms: 4.5 + -4.5 + 1.5x + x2 = 0 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + 1.5x + x2 = 0 + -4.5 1.5x + x2 = 0 + -4.5 Combine like terms: 0 + -4.5 = -4.5 1.5x + x2 = -4.5 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = -4.5 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = -4.5 + 0.5625 Combine like terms: -4.5 + 0.5625 = -3.9375 0.5625 + 1.5x + x2 = -3.9375 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = -3.9375 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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