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Simplifying (x2 + 3x) + -8(x2 + 3x) + -20 = 0 Reorder the terms: (3x + x2) + -8(x2 + 3x) + -20 = 0 Remove parenthesis around (3x + x2) 3x + x2 + -8(x2 + 3x) + -20 = 0 Reorder the terms: 3x + x2 + -8(3x + x2) + -20 = 0 3x + x2 + (3x * -8 + x2 * -8) + -20 = 0 3x + x2 + (-24x + -8x2) + -20 = 0 Reorder the terms: -20 + 3x + -24x + x2 + -8x2 = 0 Combine like terms: 3x + -24x = -21x -20 + -21x + x2 + -8x2 = 0 Combine like terms: x2 + -8x2 = -7x2 -20 + -21x + -7x2 = 0 Solving -20 + -21x + -7x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(20 + 21x + 7x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(20 + 21x + 7x2)' equal to zero and attempt to solve: Simplifying 20 + 21x + 7x2 = 0 Solving 20 + 21x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 2.857142857 + 3x + x2 = 0 Move the constant term to the right: Add '-2.857142857' to each side of the equation. 2.857142857 + 3x + -2.857142857 + x2 = 0 + -2.857142857 Reorder the terms: 2.857142857 + -2.857142857 + 3x + x2 = 0 + -2.857142857 Combine like terms: 2.857142857 + -2.857142857 = 0.000000000 0.000000000 + 3x + x2 = 0 + -2.857142857 3x + x2 = 0 + -2.857142857 Combine like terms: 0 + -2.857142857 = -2.857142857 3x + x2 = -2.857142857 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = -2.857142857 + 2.25 Reorder the terms: 2.25 + 3x + x2 = -2.857142857 + 2.25 Combine like terms: -2.857142857 + 2.25 = -0.607142857 2.25 + 3x + x2 = -0.607142857 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = -0.607142857 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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