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Simplifying 40x = (x + 5)(7x + 6) Reorder the terms: 40x = (5 + x)(7x + 6) Reorder the terms: 40x = (5 + x)(6 + 7x) Multiply (5 + x) * (6 + 7x) 40x = (5(6 + 7x) + x(6 + 7x)) 40x = ((6 * 5 + 7x * 5) + x(6 + 7x)) 40x = ((30 + 35x) + x(6 + 7x)) 40x = (30 + 35x + (6 * x + 7x * x)) 40x = (30 + 35x + (6x + 7x2)) Combine like terms: 35x + 6x = 41x 40x = (30 + 41x + 7x2) Solving 40x = 30 + 41x + 7x2 Solving for variable 'x'. Reorder the terms: -30 + 40x + -41x + -7x2 = 30 + 41x + 7x2 + -30 + -41x + -7x2 Combine like terms: 40x + -41x = -1x -30 + -1x + -7x2 = 30 + 41x + 7x2 + -30 + -41x + -7x2 Reorder the terms: -30 + -1x + -7x2 = 30 + -30 + 41x + -41x + 7x2 + -7x2 Combine like terms: 30 + -30 = 0 -30 + -1x + -7x2 = 0 + 41x + -41x + 7x2 + -7x2 -30 + -1x + -7x2 = 41x + -41x + 7x2 + -7x2 Combine like terms: 41x + -41x = 0 -30 + -1x + -7x2 = 0 + 7x2 + -7x2 -30 + -1x + -7x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 -30 + -1x + -7x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(30 + x + 7x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(30 + x + 7x2)' equal to zero and attempt to solve: Simplifying 30 + x + 7x2 = 0 Solving 30 + x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 4.285714286 + 0.1428571429x + x2 = 0 Move the constant term to the right: Add '-4.285714286' to each side of the equation. 4.285714286 + 0.1428571429x + -4.285714286 + x2 = 0 + -4.285714286 Reorder the terms: 4.285714286 + -4.285714286 + 0.1428571429x + x2 = 0 + -4.285714286 Combine like terms: 4.285714286 + -4.285714286 = 0.000000000 0.000000000 + 0.1428571429x + x2 = 0 + -4.285714286 0.1428571429x + x2 = 0 + -4.285714286 Combine like terms: 0 + -4.285714286 = -4.285714286 0.1428571429x + x2 = -4.285714286 The x term is x. 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. 0.1428571429x + 0.25 + x2 = -4.285714286 + 0.25 Reorder the terms: 0.25 + 0.1428571429x + x2 = -4.285714286 + 0.25 Combine like terms: -4.285714286 + 0.25 = -4.035714286 0.25 + 0.1428571429x + x2 = -4.035714286 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -4.035714286 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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