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Simplifying 4(x + 4)(x + 4) = 6(x + -2) Reorder the terms: 4(4 + x)(x + 4) = 6(x + -2) Reorder the terms: 4(4 + x)(4 + x) = 6(x + -2) Multiply (4 + x) * (4 + x) 4(4(4 + x) + x(4 + x)) = 6(x + -2) 4((4 * 4 + x * 4) + x(4 + x)) = 6(x + -2) 4((16 + 4x) + x(4 + x)) = 6(x + -2) 4(16 + 4x + (4 * x + x * x)) = 6(x + -2) 4(16 + 4x + (4x + x2)) = 6(x + -2) Combine like terms: 4x + 4x = 8x 4(16 + 8x + x2) = 6(x + -2) (16 * 4 + 8x * 4 + x2 * 4) = 6(x + -2) (64 + 32x + 4x2) = 6(x + -2) Reorder the terms: 64 + 32x + 4x2 = 6(-2 + x) 64 + 32x + 4x2 = (-2 * 6 + x * 6) 64 + 32x + 4x2 = (-12 + 6x) Solving 64 + 32x + 4x2 = -12 + 6x Solving for variable 'x'. Reorder the terms: 64 + 12 + 32x + -6x + 4x2 = -12 + 6x + 12 + -6x Combine like terms: 64 + 12 = 76 76 + 32x + -6x + 4x2 = -12 + 6x + 12 + -6x Combine like terms: 32x + -6x = 26x 76 + 26x + 4x2 = -12 + 6x + 12 + -6x Reorder the terms: 76 + 26x + 4x2 = -12 + 12 + 6x + -6x Combine like terms: -12 + 12 = 0 76 + 26x + 4x2 = 0 + 6x + -6x 76 + 26x + 4x2 = 6x + -6x Combine like terms: 6x + -6x = 0 76 + 26x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(38 + 13x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(38 + 13x + 2x2)' equal to zero and attempt to solve: Simplifying 38 + 13x + 2x2 = 0 Solving 38 + 13x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 19 + 6.5x + x2 = 0 Move the constant term to the right: Add '-19' to each side of the equation. 19 + 6.5x + -19 + x2 = 0 + -19 Reorder the terms: 19 + -19 + 6.5x + x2 = 0 + -19 Combine like terms: 19 + -19 = 0 0 + 6.5x + x2 = 0 + -19 6.5x + x2 = 0 + -19 Combine like terms: 0 + -19 = -19 6.5x + x2 = -19 The x term is 6.5x. Take half its coefficient (3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. 6.5x + 10.5625 + x2 = -19 + 10.5625 Reorder the terms: 10.5625 + 6.5x + x2 = -19 + 10.5625 Combine like terms: -19 + 10.5625 = -8.4375 10.5625 + 6.5x + x2 = -8.4375 Factor a perfect square on the left side: (x + 3.25)(x + 3.25) = -8.4375 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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