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Simplifying (-1x2 + 4x + -6) + -1(3x2 + 5x + 2) = 0 Reorder the terms: (-6 + 4x + -1x2) + -1(3x2 + 5x + 2) = 0 Remove parenthesis around (-6 + 4x + -1x2) -6 + 4x + -1x2 + -1(3x2 + 5x + 2) = 0 Reorder the terms: -6 + 4x + -1x2 + -1(2 + 5x + 3x2) = 0 -6 + 4x + -1x2 + (2 * -1 + 5x * -1 + 3x2 * -1) = 0 -6 + 4x + -1x2 + (-2 + -5x + -3x2) = 0 Reorder the terms: -6 + -2 + 4x + -5x + -1x2 + -3x2 = 0 Combine like terms: -6 + -2 = -8 -8 + 4x + -5x + -1x2 + -3x2 = 0 Combine like terms: 4x + -5x = -1x -8 + -1x + -1x2 + -3x2 = 0 Combine like terms: -1x2 + -3x2 = -4x2 -8 + -1x + -4x2 = 0 Solving -8 + -1x + -4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(8 + x + 4x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(8 + x + 4x2)' equal to zero and attempt to solve: Simplifying 8 + x + 4x2 = 0 Solving 8 + x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2 + 0.25x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + 0.25x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 0.25x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 0.25x + x2 = 0 + -2 0.25x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 0.25x + x2 = -2 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. 0.25x + 0.25 + x2 = -2 + 0.25 Reorder the terms: 0.25 + 0.25x + x2 = -2 + 0.25 Combine like terms: -2 + 0.25 = -1.75 0.25 + 0.25x + x2 = -1.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -1.75 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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