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Simplifying -3x2 + 5x + -8 = 2x + 6(x + 4) Reorder the terms: -8 + 5x + -3x2 = 2x + 6(x + 4) Reorder the terms: -8 + 5x + -3x2 = 2x + 6(4 + x) -8 + 5x + -3x2 = 2x + (4 * 6 + x * 6) -8 + 5x + -3x2 = 2x + (24 + 6x) Reorder the terms: -8 + 5x + -3x2 = 24 + 2x + 6x Combine like terms: 2x + 6x = 8x -8 + 5x + -3x2 = 24 + 8x Solving -8 + 5x + -3x2 = 24 + 8x Solving for variable 'x'. Reorder the terms: -8 + -24 + 5x + -8x + -3x2 = 24 + 8x + -24 + -8x Combine like terms: -8 + -24 = -32 -32 + 5x + -8x + -3x2 = 24 + 8x + -24 + -8x Combine like terms: 5x + -8x = -3x -32 + -3x + -3x2 = 24 + 8x + -24 + -8x Reorder the terms: -32 + -3x + -3x2 = 24 + -24 + 8x + -8x Combine like terms: 24 + -24 = 0 -32 + -3x + -3x2 = 0 + 8x + -8x -32 + -3x + -3x2 = 8x + -8x Combine like terms: 8x + -8x = 0 -32 + -3x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(32 + 3x + 3x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(32 + 3x + 3x2)' equal to zero and attempt to solve: Simplifying 32 + 3x + 3x2 = 0 Solving 32 + 3x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 10.66666667 + x + x2 = 0 Move the constant term to the right: Add '-10.66666667' to each side of the equation. 10.66666667 + x + -10.66666667 + x2 = 0 + -10.66666667 Reorder the terms: 10.66666667 + -10.66666667 + x + x2 = 0 + -10.66666667 Combine like terms: 10.66666667 + -10.66666667 = 0.00000000 0.00000000 + x + x2 = 0 + -10.66666667 x + x2 = 0 + -10.66666667 Combine like terms: 0 + -10.66666667 = -10.66666667 x + x2 = -10.66666667 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. + 0.25 + x2 = -10.66666667 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = -10.66666667 + 0.25 Combine like terms: -10.66666667 + 0.25 = -10.41666667 1.25 + x2 = -10.41666667 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -10.41666667 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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