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Simplifying (4x + 16)(3 + 2x) = 10x Reorder the terms: (16 + 4x)(3 + 2x) = 10x Multiply (16 + 4x) * (3 + 2x) (16(3 + 2x) + 4x * (3 + 2x)) = 10x ((3 * 16 + 2x * 16) + 4x * (3 + 2x)) = 10x ((48 + 32x) + 4x * (3 + 2x)) = 10x (48 + 32x + (3 * 4x + 2x * 4x)) = 10x (48 + 32x + (12x + 8x2)) = 10x Combine like terms: 32x + 12x = 44x (48 + 44x + 8x2) = 10x Solving 48 + 44x + 8x2 = 10x Solving for variable 'x'. Reorder the terms: 48 + 44x + -10x + 8x2 = 10x + -10x Combine like terms: 44x + -10x = 34x 48 + 34x + 8x2 = 10x + -10x Combine like terms: 10x + -10x = 0 48 + 34x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(24 + 17x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(24 + 17x + 4x2)' equal to zero and attempt to solve: Simplifying 24 + 17x + 4x2 = 0 Solving 24 + 17x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 6 + 4.25x + x2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + 4.25x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + 4.25x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 4.25x + x2 = 0 + -6 4.25x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 4.25x + x2 = -6 The x term is 4.25x. Take half its coefficient (2.125). Square it (4.515625) and add it to both sides. Add '4.515625' to each side of the equation. 4.25x + 4.515625 + x2 = -6 + 4.515625 Reorder the terms: 4.515625 + 4.25x + x2 = -6 + 4.515625 Combine like terms: -6 + 4.515625 = -1.484375 4.515625 + 4.25x + x2 = -1.484375 Factor a perfect square on the left side: (x + 2.125)(x + 2.125) = -1.484375 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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