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Simplifying (3x + 8)(4x + 10) = 8x Reorder the terms: (8 + 3x)(4x + 10) = 8x Reorder the terms: (8 + 3x)(10 + 4x) = 8x Multiply (8 + 3x) * (10 + 4x) (8(10 + 4x) + 3x * (10 + 4x)) = 8x ((10 * 8 + 4x * 8) + 3x * (10 + 4x)) = 8x ((80 + 32x) + 3x * (10 + 4x)) = 8x (80 + 32x + (10 * 3x + 4x * 3x)) = 8x (80 + 32x + (30x + 12x2)) = 8x Combine like terms: 32x + 30x = 62x (80 + 62x + 12x2) = 8x Solving 80 + 62x + 12x2 = 8x Solving for variable 'x'. Reorder the terms: 80 + 62x + -8x + 12x2 = 8x + -8x Combine like terms: 62x + -8x = 54x 80 + 54x + 12x2 = 8x + -8x Combine like terms: 8x + -8x = 0 80 + 54x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(40 + 27x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(40 + 27x + 6x2)' equal to zero and attempt to solve: Simplifying 40 + 27x + 6x2 = 0 Solving 40 + 27x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 6.666666667 + 4.5x + x2 = 0 Move the constant term to the right: Add '-6.666666667' to each side of the equation. 6.666666667 + 4.5x + -6.666666667 + x2 = 0 + -6.666666667 Reorder the terms: 6.666666667 + -6.666666667 + 4.5x + x2 = 0 + -6.666666667 Combine like terms: 6.666666667 + -6.666666667 = 0.000000000 0.000000000 + 4.5x + x2 = 0 + -6.666666667 4.5x + x2 = 0 + -6.666666667 Combine like terms: 0 + -6.666666667 = -6.666666667 4.5x + x2 = -6.666666667 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = -6.666666667 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = -6.666666667 + 5.0625 Combine like terms: -6.666666667 + 5.0625 = -1.604166667 5.0625 + 4.5x + x2 = -1.604166667 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = -1.604166667 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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